Volume 11, issue 1 (2011)

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Relative systoles of relative-essential $2$–complexes

Karin Usadi Katz, Mikhail G Katz, Stéphane Sabourau, Steven Shnider and Shmuel Weinberger

Algebraic & Geometric Topology 11 (2011) 197–217
1 L Ambrosio, M G Katz, Flat currents modulo $p$ in metric spaces and filling radius inequalities, to appear in Comm. Math. Helv. arXiv:1004.1374
2 L Ambrosio, S Wenger, Rectifiability of flat chains in Banach spaces with coefficients in $\Z_p$, to appear in Math. Z. arXiv:1004.1374
3 I Babenko, F Balacheff, Distribution of the systolic volume of homology classes arXiv:1009.2835
4 F Balacheff, A local optimal diastolic inequality on the two-sphere, J. Topol. Anal. 2 (2010) 109 MR2646992
5 V Bangert, M G Katz, S Shnider, S Weinberger, $E_7$, Wirtinger inequalities, Cayley $4$–form, and homotopy, Duke Math. J. 146 (2009) 35 MR2475399
6 M Belolipetsky, S Thomson, Systoles of hyperbolic manifolds arXiv:1008.2646
7 M Berger, What is$\ldots$a systole?, Notices Amer. Math. Soc. 55 (2008) 374 MR2382824
8 J Bochnak, M Coste, M F Roy, Real algebraic geometry, \ Ergebnisse der Math. und ihrer Grenzgebiete (3) 36, Springer (1998) MR1659509
9 M Brunnbauer, Filling inequalities do not depend on topology, J. Reine Angew. Math. 624 (2008) 217 MR2456630
10 M Brunnbauer, On manifolds satisfying stable systolic inequalities, Math. Ann. 342 (2008) 951 MR2443769
11 Y D Burago, V A Zalgaller, Geometric inequalities, Grund. der Math. Wissenschaften 285, Springer (1988) MR936419
12 A N Dranishnikov, M G Katz, Y B Rudyak, Small values of the Lusternik–Schnirelmann category for manifolds, Geom. Topol. 12 (2008) 1711 MR2421138
13 A N Dranishnikov, Y B Rudyak, Stable systolic category of manifolds and the cup-length, J. Fixed Point Theory Appl. 6 (2009) 165 MR2558490
14 C El Mir, The systolic constant of orientable Bieberbach $3$–manifolds arXiv:0912.3894
15 C El Mir, J Lafontaine, Sur la géométrie systolique des variétés de Bieberbach, Geom. Dedicata 136 (2008) 95 MR2443345
16 M Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983) 1 MR697984
17 L Guth, Volumes of balls in large Riemannian manifolds, to appear in Ann. of Math. $(2)$ arXiv:math/0610212
18 L Guth, Systolic inequalities and minimal hypersurfaces, Geom. Funct. Anal. 19 (2010) 1688 MR2594618
19 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
20 J J Hebda, Some lower bounds for the area of surfaces, Invent. Math. 65 (1981/82) 485 MR643566
21 K U Katz, M G Katz, Bi-Lipschitz approximation by finite-dimensional imbeddings, to appear in Geometriae Dedicata arXiv:0902.3126
22 K U Katz, M G Katz, Hyperellipticity and Klein bottle companionship in systolic geometry arXiv:0811.1717
23 M G Katz, Systolic geometry and topology, Math. Surveys and Monogr. 137, Amer. Math. Soc. (2007) MR2292367
24 M G Katz, Systolic inequalities and Massey products in simply-connected manifolds, Israel J. Math. 164 (2008) 381 MR2391156
25 M G Katz, Y B Rudyak, Bounding volume by systoles of $3$–manifolds, J. Lond. Math. Soc. $(2)$ 78 (2008) 407 MR2439632
26 M G Katz, Y B Rudyak, S Sabourau, Systoles of $2$–complexes, Reeb graph, and Grushko decomposition, Int. Math. Res. Not. (2006) MR2250017
27 M G Katz, M Schaps, U Vishne, Hurwitz quaternion order and arithmetic Riemann surfaces, to appear in Geom. Dedicata arXiv:math.RA/0701137
28 M G Katz, S Shnider, Cayley form, comass and triality isomorphisms, Israel J. Math. 178 (2010) 187
29 J W Morgan, D P Sullivan, The transversality characteristic class and linking cycles in surgery theory, Ann. of Math. $(2)$ 99 (1974) 463 MR0350748
30 A Nabutovsky, R Rotman, The length of the second shortest geodesic, Comment. Math. Helv. 84 (2009) 747 MR2534478
31 H Parlier, The homology systole of hyperbolic Riemann surfaces arXiv:1010.0358
32 P M Pu, Some inequalities in certain nonorientable Riemannian manifolds, Pacific J. Math. 2 (1952) 55 MR0048886
33 R Rotman, The length of a shortest geodesic loop at a point, J. Differential Geom. 78 (2008) 497 MR2396252
34 Y B Rudyak, S Sabourau, Systolic invariants of groups and $2$–complexes via Grushko decomposition, Ann. Inst. Fourier (Grenoble) 58 (2008) 777 MR2427510
35 S Sabourau, Asymptotic bounds for separating systoles on surfaces, Comment. Math. Helv. 83 (2008) 35 MR2365407
36 S Sabourau, Local extremality of the Calabi–Croke sphere for the length of the shortest closed geodesic, J. London Math. Soc. 82 (2010) 549
37 R Schoen, S T Yau, Incompressible minimal surfaces, three-dimensional manifolds with nonnegative scalar curvature, and the positive mass conjecture in general relativity, Proc. Nat. Acad. Sci. U.S.A. 75 (1978) 2567 MR496776
38 R Schoen, S T Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979) 159 MR535700
39 D P Sullivan, Triangulating and smoothing homotopy equivalences and homeomorphisms. Geometric Topology Seminar Notes, from: "The Hauptvermutung book", $K$–Monogr. Math. 1, Kluwer Acad. Publ. (1996) 69 MR1434103
40 S Wenger, A short proof of Gromov's filling inequality, Proc. Amer. Math. Soc. 136 (2008) 2937 MR2399061
41 B White, The deformation theorem for flat chains, Acta Math. 183 (1999) 255 MR1738045