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 lp 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.: E7, Wirtinger inequalities, Cayley 4-form, and homotopy. Duke Math. J. 146 ('09), no. 1, 35-70. See
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
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
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.
2. Dranishnikov, A.; Katz, M.; Rudyak, Y.: Small values of the Lusternik-Schnirelmann category for manifolds. See
april '08
Elmir, C.; Lafontaine, J.: Sur la géométrie systolique des variétés de Bieberbach. See
march '08
1. Horowitz, C.; Katz, Karin Usadi; Katz, M.: Loewner's torus inequality with isosystolic defect. Journal of Geometric Analysis, to appear. See
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
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,
july '07
A systolic lower bound for the area of CAT(0) surfaces,
june '07
1. Notes on Gromov's systolic estimate,
2. Gromov's book was out of print, but no more! Order the
3. Unlike optimal systolic constants, optimal filling constants are
independent of the topology of the manifold,
4. A study of small values of Lusternik-Schnirelmann and systolic
categories for manifolds,
5. Spines and systoles for Teichmuller space of flat tori
6. Visit the page on
may '07
1. Systolic groups acting on complexes with no flats are
word-hyperbolic, by
2. An approach to understanding the mapping class group via the
systole function on the moduli space is proposed
april '07
1. A study of filling invariants in systolic complexes and groups,
2. An effective algorithm to determine the systolic loops of a
hyperbolic surface,
march '07
1. A short proof of Gromov's filling inequality,
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,
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,