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arXiv · 2106.10677

Bounds on Systoles and Homotopy Complexity

Tsachik Gelander·Paul Vollrath
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Abstract

We give an elementary proof of a weak variant of the homotopy type conjecture from [Gel04]. The proof relies on Belolipetskys estimate on the systole in terms of the volume which is a consequence of Prasads volume formula. In particular we extend the estimate established in [B20] for hyperbolic manifolds to general arithmetic manifolds.

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Tsachik Gelander, Paul Vollrath. 2021-06-20. Bounds on Systoles and Homotopy Complexity. https://arxiv.org/abs/2106.10677

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