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2011 Relative systoles of relative-essential $2$–complexes
Karin Usadi Katz, Mikhail G Katz, Stéphane Sabourau, Steven Shnider, Shmuel Weinberger
Algebr. Geom. Topol. 11(1): 197-217 (2011). DOI: 10.2140/agt.2011.11.197

Abstract

We prove a systolic inequality for a ϕ–relative systole of a ϕ–essential 2–complex X, where ϕ:π1(X)G is a homomorphism to a finitely presented group G. Thus, we show that universally for any ϕ–essential Riemannian 2–complex X, and any G, the following inequality is satisfied: sys(X,ϕ)28Area(X). Combining our results with a method of L Guth, we obtain new quantitative results for certain 3–manifolds: in particular for the Poincaré homology sphere Σ, we have sys(Σ)324Vol(Σ).

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Karin Usadi Katz. Mikhail G Katz. Stéphane Sabourau. Steven Shnider. Shmuel Weinberger. "Relative systoles of relative-essential $2$–complexes." Algebr. Geom. Topol. 11 (1) 197 - 217, 2011. https://doi.org/10.2140/agt.2011.11.197

Information

Received: 27 October 2009; Revised: 12 July 2010; Accepted: 2 October 2010; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1228.53056
MathSciNet: MR2764040
Digital Object Identifier: 10.2140/agt.2011.11.197

Subjects:
Primary: 53C23, 57M20
Secondary: 57N65

Rights: Copyright © 2011 Mathematical Sciences Publishers

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