Relative systoles of relative-essential 2-complexes

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).

20 pages, to appear in Algebraic and Geometric Topology

References in corpus (6)

• Hyperellipticity and Klein bottle companionship in systolic geometry
• Systolic volume of homology classes
• Cayley 4-form, comass, and triality isomorphisms
• Bi-Lipschitz approximation by finite-dimensional imbeddings
• Rectifiability of flat chains in Banach spaces with coefficients in $Z_p$
• The homology systole of hyperbolic Riemann surfaces

Cited by in corpus (1)

• Cohomological dimension, self-linking, and systolic geometry