The Hopf invariant and simplex straightening

2007/09/09 by Larry Guth, Guth, Larry · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:53C23 #msc:57M50

paper · pdf · doi:10.48550/arxiv.0709.1247

17 pages. In the first version of the paper, there was a mistake on page 6 in the proof of Lemma 1. The paper is corrected, and some parts have been simplified

arxiv created 2009/03/16 · arxiv updated 2009/12/01

Abstract

Let M be a closed 3-manifold which can be triangulated with N simplices. We prove that any map from M to a genus 2 surface has Hopf invariant at most C^N. Let X be a closed oriented hyperbolic 3-manifold with injectivity radius less than epsilon at one point. If there is a degree non-zero map from M to X, then we prove that epsilon is at least C^-N.

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• Isoperimetric inequalities and rational homotopy invariants

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