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Relative systoles of
relative-essential $2$–complexes
Karin Usadi Katz, Mikhail G Katz, Stéphane Sabourau, Steven Shnider and Shmuel Weinberger |
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Algebraic & Geometric Topology 11 (2011) 197–217
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Abstract |
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We prove a systolic inequality for a –relative systole of a –essential –complex , where is a homomorphism to a finitely presented group . Thus, we show that universally for any –essential Riemannian –complex , and any , the following inequality is satisfied: . Combining our results with a method of L Guth, we obtain new quantitative results for certain –manifolds: in particular for the Poincaré homology sphere , we have . |
Keywords
coarea formula, cohomology of cyclic groups, essential
complex, Grushko's theorem, Poincaré duality, systole,
systolic ratio
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Mathematical Subject Classification 2000
Primary: 53C23, 57M20
Secondary: 57N65
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References |
Publication
Received: 27 October 2009
Revised: 12 July 2010
Accepted: 2 October 2010
Published: 7 January 2011
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Authors |
| Karin Usadi Katz | |
| Department of Mathematics Bar Ilan University 52900 Ramat Gan Israel |
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| Mikhail G Katz | |
| Department of Mathematics Bar Ilan University 52900 Ramat Gan Israel |
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| http://u.cs.biu.ac.il/~katzmik/sgtdirectory/katz.html | |
| Stéphane Sabourau | |
| Laboratoire de Mathématiques et
Physique Théorique Université de Tours Parc de Grandmont 37200 Tours France |
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| http://www.lmpt.univ-tours.fr/~sabourau/ | |
| Steven Shnider | |
| Department of Mathematics Bar Ilan University 52900 Ramat Gan Israel |
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| Shmuel Weinberger | |
| Department of Mathematics University of Chicago 5734 S University Avenue Chicago IL 60637-1514 United States |
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| http://www.math.uchicago.edu/~shmuel/ | |
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