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arXiv · 0709.1247

The Hopf invariant and simplex straightening

Larry Guth
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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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Larry Guth. 2009-03-16. The Hopf invariant and simplex straightening. https://arxiv.org/abs/0709.1247

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