Amenable open covers and simplicial volume of manifolds with boundary

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• Pietro Capovilla, SNS Pisa
• Friday 24 January 2025, 13:45-14:45
• MR13.

If you have a question about this talk, please contact Macarena Arenas.

Simplicial volume is a non-negative real number which is invariant under homotopy equivalences between closed manifolds. It was introduced by Gromov as an obstruction on the possible geometries a given manifold can support. One of the strongest vanishing results for simplicial volume of closed manifolds is in presence of amenable open covers with small multiplicity. I will discuss some conditions under which this result can be extended to manifolds with boundary, inspired by the recent work of Li, Löh, Moraschini and Raptis. To this end, I will follow Gromov’s original approach via the theory of multicomplexes, whose foundations have been recently laid down by Frigerio and Moraschini.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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