The Hopf invariant and simplex straightening

Details The Hopf invariant and simplex straightening The Hopf invariant and simplex straightening

2007-09-09

arxiv.org/abs/0709.1247v2

Mathematics

Differential Geometry

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, an

Scientific paper

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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