nov '18

Hugo Akrout, Bjoern Muetzel. Construction of surfaces with large
systolic ratio. See
See
https://arxiv.org/abs/1311.1449

jul '18

Local maxima of the systole function, by Maxime Fortier Bourque, Kasra
Rafi. See https://arxiv.org/abs/1807.08367

jan '18

A local systolic-diastolic inequality in contact and symplectic
geometry, by Gabriele Benedetti, Jungsoo Kang. See
https://arxiv.org/abs/1801.00539

nov '17

On growth of systole along congruence coverings of Hilbert modular
varieties,
by Plinio G P Murillo,
Algebraic & Geometric Topology 17:5 (2017), 2753-2762
https://msp.org/agt/2017/17-5/p06.xhtml

feb '16

1. Bou-Rabee, Khalid; Cornulier, Yves; Systolic growth of linear
groups. Proc. Amer. Math. Soc. 144 (2016), no. 2, 529-533.

2. Fanoni, Federica; Parlier, Hugo; Systoles and kissing numbers of finite area hyperbolic surfaces. Algebr. Geom. Topol. 15 (2015), no. 6, 3409-3433.

3. Chen, Lizhi; Li, Weiping. Systoles of surfaces and 3-manifolds. Geometry and topology of submanifolds and currents, 61-80, Contemp. Math., 646, Amer. Math. Soc., Providence, RI, 2015.

4. Grácio, Clara. Systoles on compact Riemann surfaces with symbolic dynamics. Nonlinear maps and their applications, 269-288, Springer Proc. Math. Stat., 112, Springer, Cham, 2015.

june '15

1. arXiv:1506.09051
Regular geometric cycles.
Guillaume Bulteau

2. arXiv:1506.08341
Systolic Surfaces of Arithmetic Hyperbolic 3-Manifolds.
Benjamin Linowitz, Jeffrey S. Meyer

3. arXiv:1506.07848
Systolic geometry and regularization technique.
Guillaume Bulteau

4. arXiv:1506.07121
Combinatorial systolic inequalities.
Ryan Kowalick, Jean-François Lafont, Barry Minemyer

april '15

1. Elsner, Tomasz; Januszkiewicz, Tadeusz; Homotopical systole and
hyperbolicity. Bull. Lond. Math. Soc. 47 (2015), no. 2, 203-205.

2. Katz, Mikhail G.; Sabourau, Stephane; Dyck's surfaces, systoles,
and capacities. Trans. Amer. Math. Soc. 367 (2015), no. 6, 4483-4504.

3. Chepoi, Victor; Osajda, Damian Dismantlability of weakly systolic
complexes and applications. Trans. Amer. Math. Soc. 367 (2015),
no. 2, 1247-1272.

4. Zachos, Anastasios N. Minimal systolic circles. J. Convex Anal. 21
(2014), no. 3, 619-650.

5. Mondal, Sugata Systole and \lambda_{2g-2} of closed hyperbolic
surfaces of genus g. Enseign. Math. 60 (2014), no. 1-2, 3-24.

6. Chen, Lizhi; Systolic freedom of 3-manifolds. Thesis (Ph.D.)
Oklahoma State University. 2014. 83 pp.

june '14

Lizhi Chen. Z_2-coefficient Homology (1,2)-systolic Freedom of RP^3#RP^3. http://arxiv.org/abs/1402.4504

may '14

1. Karin Katz, Mikhail Katz, Michael Schein, Uzi Vishne. Bolza quaternion order and asymptotics of systoles along congruence subgroups. See http://arxiv.org/abs/1405.5454

2. Larry Guth, Alexander Lubotzky. Quantum error-correcting codes and 4-dimensional arithmetic hyperbolic manifolds. See http://arxiv.org/abs/1310.5555

apr '14

1. Systoles and Dehn surgery for hyperbolic 3-manifolds

Grant S
Lakeland and Christopher J Leininger

Algebraic & Geometric
Topology 14 (2014) 1441-1460 DOI: 10.2140/agt.2014.14.1441

Abstract. Given a closed hyperbolic 3-manifold M of volume V, and a
link L in M such that the complement M\L is hyperbolic, we establish a
bound for the systole length of M\L in terms of V. This extends a
result of Adams and Reid, who showed that in the case that M is not
hyperbolic, there is a universal bound of 7.35534... As part of the
proof, we establish a bound for the systole length of a noncompact
finite volume hyperbolic manifold which grows asymptotically like 4/3
logV.

2. Massart, Daniel; Muetzel, Bjoern. On the intersection form of surfaces. Manuscripta Math. 143 (2014), no. 1-2, 19-49. See http://www.ams.org/mathscinet-getitem?mr=3147443

jun '13

Belolipetsky, Mikhail; On 2-Systoles of Hyperbolic 3-Manifolds. Geom. Funct. Anal. 23 (2013), no. 3, 813-827. See http://www.ams.org/mathscinet-getitem?mr=3061772

may '13

On the finite dimensional approximation of the Kuratowski-embedding
for compact manifolds

Malte Roeer
http://arxiv.org/abs/1305.1529

nov '12

Sara Fernandes, Clara Gracio, Carlos Correia Ramos, Systoles in discrete dynamical systems, Journal of Geometry and Physics, Volume 63, January 2013, Pages 129-139. See http://www.sciencedirect.com/science/article/pii/S0393044012001854

oct '12

1. Liokumovich, Yevgeny; Spheres of small diameter with long sweep-outs. Proc. Amer. Math. Soc. 141 (2013), no. 1, 309-312. http://www.ams.org/mathscinet-getitem?mr=2988732

2. Filippo Cerocchi: Margulis Lemma, entropy and free products. See http://arxiv.org/abs/1204.1619

3. Chady El Mir, Zeina Yassine: Conformal Geometric Inequalities on the Klein Bottle. See http://arxiv.org/abs/1209.6202

sep '12

http://arxiv.org/abs/1209.1783 Exotic arithmetic structure on the first Hurwitz triplet, by Lei Yang

july '12

1. Nabutovsky, Alexander; Rotman, Regina: Linear bounds for lengths of geodesic loops on Riemannian 2-spheres. J. Differential Geom. 89 (2011), no. 2, 217-232.

2. Hwang, Jun-Muk; To, Wing-Keung: Injectivity radius and gonality of a compact Riemann surface. Amer. J. Math. 134 (2012), no. 1, 259--283.

3. Gournay, Antoine: Widths of l^{p} balls. Houston
J. Math. 37 (2011), no. 4, 1227-1248.

4. De Pauw, Thierry; Hardt, Robert: Rectifiable and flat G chains in a metric space. Amer. J. Math. 134 (2012), no. 1, 1-69.

5.
http://arxiv.org/abs/1206.2965

A Note on Riemann Surfaces of Large Systole

Shotaro Makisumi

We examine the large systole problem, which concerns compact
hyperbolic Riemannian surfaces whose systole, the length of the
shortest noncontractible loops, grows logarithmically in genus. The
generalization of a construction of Buser and Sarnak by Katz, Schaps,
and Vishne, which uses principal "congruence" subgroups of a fixed
cocompact arithmetic Fuchsian, achieves the current maximum known
growth constant of \gamma = 4/3. We prove that this is the best
possible value of \gamma for this construction using arithmetic
Fuchsians in the congruence case. The final section compares the large
systole problem with the analogous large girth problem for regular
graphs.

may '12

1. Philippe, Emmanuel: Détermination géométrique de la systole des groupes de triangles. (French) [Geometric determination of the systole of triangle groups] C. R. Math. Acad. Sci. Paris 349 (2011), no. 21-22, 1183--1186.

2. On 2-systoles of hyperbolic 3-manifolds, by Mikhail Belolipetsky, arXiv:1205.5198

3. Dyck's surfaces, systoles, and capacities. By Mikhail G. Katz and Stephane Sabourau. See http://arxiv.org/abs/1205.0188

jan '12

1. Hyperellipticity and Systoles of Klein Surfaces. By Mikhail G. Katz and Stephane Sabourau. See http://www.ams.org/mathscinet-getitem?mr=2944532 and http://arxiv.org/abs/1201.0361

2. Makover, Eran; McGowan, Jeffrey: The length of closed geodesics on random Riemann surfaces. Geom. Dedicata 151 (2011), 207--220. See mathscinet at http://www.ams.org/mathscinet-getitem?mr=2780746

3. Belolipetsky, Mikhail V.; Thomson, Scott A. Systoles of hyperbolic manifolds. Algebr. Geom. Topol. 11 (2011), no. 3, 1455--1469 at http://dx.doi.org/10.2140/agt.2011.11.1455 and mathscinet at http://www.ams.org/mathscinet-getitem?mr=2821431

aug '11

http://arxiv.org/abs/1108.2886

Title: Homological Error Correcting Codes and Systolic Geometry

Authors: Ethan Fetaya

Geometry & Topology 15 (2011) 1477-1508

Isosystolic genus three surfaces critical for slow metric variations

by Stephane Sabourau

URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p037.xhtml

DOI: 10.2140/gt.2011.15.1477

july '11

1. arXiv:1107.5975

Title: Systole et rayon maximal des varietes hyperboliques non compactes

Authors: Matthieu Gendulphe

2. Makover, Eran; McGowan, Jeffrey: The length of closed geodesics on random Riemann surfaces. Geom. Dedicata 151 (2011), 207--220.

3. Langer, Joel C.; Singer, David A.:
When is a curve an octahedron?

Amer. Math. Monthly 117 (2010), no. 10, 889--902.

4. Erickson, Jeff; Worah, Pratik: Computing the shortest essential
cycle.

Discrete Comput. Geom. 44 (2010), no. 4, 912--930.

see
http://www.springerlink.com/content/e3g565771qh460n6/

june '11

1. If you are in Germany, you may be interested in Pape's course, see http://www.uni-math.gwdg.de/pape/teaching.html

2.
arXiv:1106.1834

Title: Geodesics, volumes and Lehmer's conjecture

Author: Mikhail
Belolipetsky

3. Algebraic & Geometric Topology 11 (2011) 1455-1469

Systoles of hyperbolic manifolds

by Mikhail V Belolipetsky and Scott A Thomson

URL:
http://www.msp.warwick.ac.uk/agt/2011/11-03/p048.xhtml

DOI: 10.2140/agt.2011.11.1455

may '11

arXiv:1105.0553

Title: Liouville's equation for curvature and systolic defect

Author: Mikhail Katz

apr '11

Algebraic & Geometric Topology 11 (2011) 983-999

Stable systolic category of the product of spheres

by Hoil Ryu

URL:
http://www.msp.warwick.ac.uk/agt/2011/11-02/p030.xhtml

DOI: 10.2140/agt.2011.11.983

mar '11

1. Balacheff ; Sabourau : Diastolic and isoperimetric inequalities on surfaces. Ann. Sci. Ec. Norm. Super. (4) 43 (2010), no. 4, 579--605. See mathscinet entry

2. Guth, Larry : Volumes of balls in large Riemannian manifolds. Annals of Mathematics 173 (2011), no. 1, 51--76. See arXiv:math.DG/0610212 and mathscinet entry

jan '11

Taylor, Laurence R.
:
Controlling indeterminacy in Massey triple products. Geom. Dedicata
148 (2010), 371--389.
Taylor constructs interesting manifolds possessing nontrivial Massey
triple products, leading to new examples of systolic inequalities
based on:
Systolic inequalities and Massey products in
simply-connected manifolds. *Israel J. Math.* 164 ('08),
381-395. See
arXiv:math.DG/0604012.

nov '10

arXiv:1011.2962

Title: Short loop decompositions of surfaces and the geometry of Jacobians

Authors: Florent Balacheff, Hugo Parlier, Stephane Sabourau

oct '10

arXiv:1010.0358

Title: The homology systole of hyperbolic Riemann surfaces

Authors: Hugo Parlier

sep '10

1. arXiv:1009.2835

Title: Distribution of the systolic volume of homology classes

Authors:
Ivan K. Babenko,
Florent Balacheff,

aug '10

arXiv:1008.2646

Title: Systoles of Hyperbolic Manifolds

Authors:
Mikhail Belolipetsky,
Scott A. Thomson

july '10

1. arXiv:1007.2913 [pdf, ps, other]

Title: Stable systolic category of the product of spheres

Authors: Hoil Ryu

2. arXiv:1007.0877

Title: Conformal isosystolic inequality of Bieberbach 3-manifolds

Authors: Chady El Mir

april '10

arXiv:1004.1374

Title: Flat currents modulo p in metric spaces and filling radius inequalities

Authors: Luigi Ambrosio, Mikhail G. Katz

march '10

arXiv:1003.4247

Title: Metaphors in systolic geometry

Author:
Larry Guth

december '09

1. Gendulphe, Matthieu: D ecoupages et in egalit es systoliques pour les surfaces hyperboliques a bord. (French. French summary) [Systolic cuttings and inequalities for surfaces with boundary] Geom. Dedicata 142 (2009), 23--35.

2. arXiv:0912.3894

Title: The systolic constant of orientable Bieberbach 3-manifolds

Authors: Chady Elmir

3. arXiv:0912.3413

Title: Infinitesimal Systolic Rigidity of Metrics all of whose
Geodesics are Closed and of the same Length

Authors: J.-C. Alvarez Paiva, F. Balacheff

4. Dranishnikov, A.; Rudyak, Y.: Stable systolic category of manifolds and the cup-length. Journal of Fixed Point Theory and Applications 6 (2009), no. 1, 165-177.

november '09

1. Gromov, M.: Singularities, Expanders and Topology of Maps. Part 1: Homology Versus Volume in the Spaces of Cycles. Journal Geometric And Functional Analysis (GAFA). Online SpringerLink November 03, 2009. (Systolic matters are dealt with on pages 92-94.)

2. arXiv:0911.4265

Title: Relative systoles of relative-essential 2-complexes

Authors: Karin U. Katz, Mikhail G. Katz, Stephane Sabourau, Steven Shnider,
Shmuel Weinberger

october '09

arXiv:0910.2257

Title: Filling minimality of Finslerian 2-discs

Author:
Sergei Ivanov

september '09

1. Mikhail Gromov. Bull. Lond. Math. Soc. 41 (2009), no. 3, 573--575.

In '08, the London Mathematical Society has elected Professor Mikhail
Gromov to Honorary Membership of the Society, noting in particular:
"His bound on the length of the shortest non-contractible loop of a
Riemannian manifold, the systole, together with his new invariant, the
filling radius, created systolic geometry in its modern form."

2. arXiv:0909.1966

Title: Small filling sets of curves on a surface

Authors: James W. Anderson, Hugo Parlier, Alexandra Pettet

3. arXiv:0909.1665

Title: Area-minimizing projective planes in three-manifolds

Authors: H. Bray, S. Brendle, M. Eichmair, A. Neves

july '09

1. arXiv:0907.3517

Title: Scattering at low energies on manifolds with cylindrical ends
and stable systoles

Authors: Werner Muller, Alexander Strohmaier

2. arXiv:0907.2223

Title: Local extremality of the Calabi-Croke sphere for the length of
the shortest closed geodesic

Author: Stephane Sabourau

april '09

Babenko, Ivan: Addenda a l'article intitule ``Topologie des systoles unidmensionnelles'' [Addenda to the article titled ``Topology of one-dimensional systoles''] Enseign. Math. (2) 54 (2008), no. 3-4, 397--398.

march '09

arXiv:0903.5299, Title: Systolic inequalities and minimal hypersurfaces, by Larry Guth

february '09

1. Katz, Karin Usadi; Katz, M.: Bi-Lipschitz approximation by finite-dimensional imbeddings. See arXiv:0902.3126 More details may be found at hyperreals

2. Brunnbauer, Michael: Filling inequalities do not depend on topology. J. Reine Angew. Math. 624 (2008), 217--231. See Brunnbauer

3. Pettet, Alexandra; Souto, Juan: Minimality of the well-rounded retract. Geom. Topol. 12 (2008), no. 3, 1543--1556.

4. Brunnbauer, Michael: Homological invariance for asymptotic invariants and systolic inequalities. Geom. Funct. Anal. 18 (2008), no. 4, 1087--1117. See Brunnbauer

january '09

Bangert, V; Katz, M.; Shnider, S.; Weinberger, S.: E_{7},
Wirtinger inequalities, Cayley 4-form, and homotopy. Duke
Math. J. 146 ('09), no. 1, 35-70. See
arXiv:math.DG/0608006.

december '08

arXiv:0812.4637: Stable Systolic Category of Manifolds and the Cup-length. Authors: Alexander N. Dranishnikov, Yuli B. Rudyak

november '08

1. Balacheff, F.: A local optimal diastolic inequality on the
two-sphere. See
arXiv:0811.0330

The author applies Loewner's torus inequality to the ramified triple
cover of the sphere, so as to prove a local minimality of Calabi's
"triangular pillow" metric for the least length of a geodesic loop.

2. Katz, Karin Usadi; Katz, M.: Hyperellipticity and Klein bottle companionship in systolic geometry. See arXiv:0811.1717

3. Parlier, Hugo: Fixed-point free involutions on Riemann surfaces. Israel J. Math. 166 ('08), 297-311. arXiv:math.DG/0504109

october '08

1. Martelli, Bruno: Complexity of PL-manifolds. See arXiv:0810.5478

september '08

1. Croke, C.: Small volume on big n-spheres,
Proc. Amer. Math. Soc. 136 (2008), no. 2, 715-717
mathscinet review

It is known that an n-sphere with a metric invariant by the antipodal
involution, admits a curvature-free volume lower bound in terms of the
least distance L between a point and its antipodal image (the bound
follows from Gromov's filling inequality from '83, applied to the
quotient real projective n-space). The paper shows that in the
absence of the condition of invariance by the antipodal map, the total
volume is no longer constrained by L.

2. Rudyak, Yuli B.; Sabourau, Stéphane: Systolic invariants of groups and 2-complexes via Grushko decomposition. Ann. Inst. Fourier (Grenoble) 58 (2008), no. 3, 777--800 mathscinet

august '08

1. arXiv:0807.5040 Cohomological dimension, self-linking, and systolic geometry, by Dranishnikov, A.; Katz, M.; Rudyak, Y.

july '08

1. Bounding volume by systoles of 3-manifolds, Mikhail G. Katz; Yuli B. Rudyak in Journal of the London Mathematical Society 2008; doi: 10.1112/jlms/jdm105

2. Asymptotic properties of coverings in negative curvature, Andrea Sambusetti in Geometry & Topology 12 (2008) 617-637.

june '08

1. Frequently Asked Questions about Journal of the London Mathematical Society

may '08

1. Neil's theology and systoles

2. Dranishnikov, A.; Katz, M.; Rudyak, Y.: Small values of the Lusternik-Schnirelmann category for manifolds. See arXiv:0805.1527

april '08

Elmir, C.; Lafontaine, J.: Sur la géométrie systolique des variétés de Bieberbach. See arXiv:0804.1419

march '08

1. Horowitz, C.; Katz, Karin Usadi; Katz, M.: Loewner's torus inequality with isosystolic defect. Journal of Geometric Analysis, to appear. See arXiv:0803.0690

2. Berger, M.: What is... a Systole? Notices of the AMS 55 (2008), no. 3, 374-376.

3. Sabourau, S.: Asymptotic bounds for separating systoles on surfaces. Comment. Math. Helv. 83 (2008), no. 1, 35--54.

january '08

Cayley 4-form comass and triality isomorphisms, by M. Katz and S. Shnider, see arXiv:0801.0283

december '07

Systolic volume of hyperbolic manifolds and connected sums of manifolds, by S. Sabourau, Geom. Dedicata 127 (2007), 7-18.

october '07

A study of a d-systolic upper bound in terms of the log of the total
volume of a d-dimensional complex, by

Lubotzky, A.; Meshulam, R.: A Moore bound for simplicial complexes.
Bull. Lond. Math. Soc. 39 (2007), no. 3, 353--358.

august '07

On manifolds satisfying stable systolic inequalities,

by
M. Brunnbauer

july '07

A systolic lower bound for the area of CAT(0) surfaces,

by Y. Chai
and D. Lee

june '07

1. Notes on Gromov's systolic estimate,

by L. Guth

2. Gromov's book was out of print, but no more! Order the new edition now

3. Unlike optimal systolic constants, optimal filling constants are
independent of the topology of the manifold,

by
M. Brunnbauer

4. A study of small values of Lusternik-Schnirelmann and systolic
categories for manifolds,

by
A. Dranishnikov, M. Katz, and Y. Rudyak

5. Spines and systoles for Teichmuller space of flat tori

by A. Pettet and J. Souto

6. Visit the page on
simplicial nonpositive curvature,

maintained by T. Elsner

may '07

1. Systolic groups acting on complexes with no flats are
word-hyperbolic, by

by P. Przytycki.
See also
systolic group theory

2. An approach to understanding the mapping class group via the
systole function on the moduli space is proposed

by
M. Bestvina

april '07

1. A study of filling invariants in systolic complexes and groups,

by
T. Januszkiewicz and J. Świątkowski.
See also
systolic group theory

2. An effective algorithm to determine the systolic loops of a
hyperbolic surface,

by H. Akrout

march '07

1. A short proof of Gromov's filling inequality,

by S. Wenger

2. A book entitled "Systolic geometry and topology" is published by the

AMS, Mathematical Surveys and Monographs, vol. 137.

february '07

1. The systolic constant, the minimal entropy, and the spherical
volume of a manifold depend only on the image of the fundamental class
in the Eilenberg-MacLane space,

by
M. Brunnbauer

2. Finding closed geodesics, as well as loops that are nearly closed
geodesics, in a tight sweep-out of a 2-sphere,

by
T. Colding and W. Minicozzi

3. An essay by Gábor Elek on the mathematics of Mikhael Gromov,
has appeared at
Acta Math. Hungarica
.
Systoles are discussed on pages 174-175.

january '07

1. A study of the global geometry of Teichmuller space by lengths of
simple closed geodesics,

by Zheng Huang

2. A study of closed geodesics for Finsler metrics on the 2-sphere, in
relation to the theory of H. Hofer, K. Wysocki, and E. Zehnder,

by
A. Harris and G. Paternain

3. Ever wonder how short a closed geodesic can be on a hyperbolic
4-manifold? Find the answer

by I. Agol