Relative systoles of relative-essential 2-complexes

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

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We prove a systolic inequality for a Π-relative systole of a Π-essential 2-complex X, where Π: π1→ G is a homomorphism to a finitely presented group G. Thus, we show that universally for any Π-essential Riemannian 2-complex X, and any G, the following inequality is satisfied: sys(X, Π)2 ≤8Area(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)3 ≤ 24Vol(Σ).

Original languageEnglish
Pages (from-to)197-217
Number of pages21
JournalAlgebraic and Geometric Topology
Issue number1
StatePublished - 2011

Bibliographical note

cited By 5


FundersFunder number
National Science Foundation
Directorate for Mathematical and Physical Sciences0504721


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