Mapping class groups of highly connected (4k+2)-manifolds

Abstract

We compute the mapping class group of the manifolds ♯g(S2k+1×S2k+1)$$\sharp ^g(S^{2k+1}\times S^{2k+1})$$ for k>0$$k>0$$ in terms of the automorphism group of the middle homology and the group of homotopy (4k+3)$$(4k+3)$$-spheres. We furthermore identify its Torelli subgroup, determine the abelianisations, and relate our results to the group of homotopy equivalences of these manifolds.