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arXiv · 0911.4265

Relative systoles of relative-essential 2-complexes

Karin U. Katz·Mikhail G. Katz·Stephane Sabourau·Steven Shnider·Shmuel Weinberger
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Abstract

We prove a systolic inequality for the phi-relative 1-systole of a phi-essential 2-complex, where phi is a homomorphism from the fundamental group of the complex, to a finitely presented group G. Indeed we show that universally for any phi-essential Riemannian 2-complex, and any G, the area of X is bounded below by 1/8 of sys(X,phi)^2. Combining our results with a method of Larry Guth, we obtain new quantitative results for certain 3-manifolds: in particular for Sigma the Poincare homology sphere, we have sys(Sigma)^3 < 24 vol(Sigma).

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Karin U. Katz, Mikhail G. Katz, Stephane Sabourau, Steven Shnider, Shmuel Weinberger. 2009-11-22. Relative systoles of relative-essential 2-complexes. https://arxiv.org/abs/0911.4265

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