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Mapping class groups of h-cobordant manifolds

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  • UserSamuel Muñoz Echániz
  • ClockFriday 10 June 2022, 15:00-16:00
  • HouseMR16.

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Given two h-cobordant manifolds L and M, how much do (the homotopy types of) the diffeomorphism groups Diff(L) and Diff(M) differ? We will see that the homotopy groups of these two spaces are the same “up to extensions” in positive degrees in a range. Contrasting this fact, I will present an example of h-cobordant manifolds with different mapping class groups. In doing so, we will review the basics of simple homotopy theory and introduce several moduli spaces of manifolds analogous to the classifying space of diffeomorphisms BDiff(M).

This talk is part of the Junior Geometry Seminar series.

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