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Group rings and hyperbolic geometry

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  • UserGrigori Avramidi (MPIM)
  • ClockWednesday 08 May 2024, 16:00-17:00
  • HouseMR13.

If you have a question about this talk, please contact Oscar Randal-Williams .

Given a closed hyperbolic manifold M, are there lower bounds on the number of k-cells c_k(M) in a cell decomposition in terms of the geometry of the manifold? Gromov showed that if the manifold has injectivity radius at least 10^6 times (n log n), then there are at least n 1-cells, and conjectured that injectivity radius const times log n should be enough. In this talk I will describe a result providing a lower bound on the number of k-cells for each 0 < k < dim (M). The main input is a freedom theorem for ideals in group rings of hyperbolic groups, which also has other applications. Joint work with Thomas Delzant.

This talk is part of the Differential Geometry and Topology Seminar series.

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Guildhall School Lecture Recital Room, 17.30-19.30 Hicks &amp; Mead Rooms, University Centre, Granta Place McCrum Lecture Theatre, Corpus Christi College, Bene't Street (next to the Eagle pub)

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