The Hopf invariant and simplex straightening
Differential Geometry
2009-03-16 v2
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}.
Cite
@article{arxiv.0709.1247,
title = {The Hopf invariant and simplex straightening},
author = {Larry Guth},
journal= {arXiv preprint arXiv:0709.1247},
year = {2009}
}
Comments
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