Mapping class groups of highly connected manifolds, II

The classical mapping class group Γ(g) of a surface of genus g shares many features with its higher dimensional analogue Γ(g,n)—the group of isotopy classes of diffeomorphisms of #ᵍ(Sⁿ x Sⁿ)—but some aspects become easier in high dimensions. This enabled Kreck in the 70’s to describe Γ(g,n) for n>2 in terms of an arithmetic group and the group of exotic spheres. His answer, however, left open two extension problems which were later understood in some dimensions, but remained unsettled in most cases. Motivated by renewed interest in these groups in relation to moduli spaces of manifolds, I will recall Kreck’s description of Γ(g,n) and explain how to resolve the remaining extension problems completely for n odd.