Bounds on Systoles and Homotopy Complexity
Tsachik Gelander, Paul Vollrath
TL;DR
This paper provides an elementary proof of a weak homotopy type conjecture, extending systole-volume estimates from hyperbolic to general arithmetic manifolds using Prasad's volume formula.
Contribution
It introduces a simplified proof of a homotopy type conjecture and generalizes systole estimates to broader classes of arithmetic manifolds.
Findings
Elementary proof of a weak homotopy type conjecture
Extension of systole-volume estimates to general arithmetic manifolds
Connection between systole bounds and homotopy complexity
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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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Mathematical Dynamics and Fractals · Geometric and Algebraic Topology