Moduli spaces of reducible 3-manifolds

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• Jan Steinebrunner (University of Copenhagen)
• Wednesday 05 June 2024, 10:15-11:00
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TRH - Topology, representation theory and higher structures

In joint work with Rachael Boyd and Corey Bregman we study the classifying space B Diff(M) of the diffeomorphism group of a connected, compact, orientable 3-manifold M. By a theorem of Milnor every such M has a unique prime decomposition as a connected sum of prime 3-manifolds. The purpose of this talk is to explain how one can compute the moduli space B Diff(M) in terms of the moduli spaces of prime factors. We build a contractible space parametrising the systems of reducing spheres, which yields a concrete model of B Diff(M).We use this to prove that if M has non-empty boundary, then B Diff(M rel boundary) has the homotopy type of a finite CW complex, as was conjectured by Kontsevich.

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

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