Contributed talk – Mapping class groups of highly connected manifolds – Manuel Krannich (University of Cambridge)

December 6, 2018 @ 2:30 pm – 3:00 pm
Seminar Room 1
Newton Institute

The group of isotopy classes of diffeomorphisms of a highly connected almost parallelisable manifold of even dimension 2n>4 has been computed by Kreck in the late 70’s. His answer, however, left open two extension problems, which were later understood in some particular dimensions, but remained unsettled in general. In this talk, I will explain how to resolve these extension problems in the case of n being odd, resulting in a complete description of the mapping class group in question in terms of an arithmetic group and the cokernel of the stable J-homomorphism.