Volume, Complexity and Torsion

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• Raz Slutsky (University of Oxford)
• Tuesday 15 July 2025, 15:30-16:00
• Seminar Room 1, Newton Institute.

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NPCW06 - Non-positive curvature and applications

In many non-positively curved settings, the volume of a manifold controls its complexity in various ways. Many of these results are based on geometric methods and thus do not apply in the case of orbifolds, or equivalently, in the presence of torsion in the corresponding group. In this talk, I will discuss two results which try to overcome this issue. The first is a quantitative version of Selberg’s lemma, relating the co-volume of an arithmetic lattice to the minimal index of a torsion-free subgroup. The second is a bound on the Betti numbers over finite fields of negatively curved orbifolds in terms of their volume. This extends a result by Gromov. These are joint works with Tsachik Gelander and Guy Kapon.

This talk is part of the Isaac Newton Institute Seminar Series series.

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