On the mapping class groups of $#_r(S^p \times S^p)$ for $p=3,7$

Abstract

For M_r = #_r(S^p \times S^p), p=3, 7, we calculate the group of isotopy classes of orientation preserving diffeomorphisms of $M_r$ modulo isotopy classes with representatives which are the identity outside a 2p-disc and also the group of homotopy classes of orientation preserving homotopy equivalences of M_r.

arXiv commentPresentation significantly improved following referee's comments; e.g. added Corollary 2.8 to make certain classes in the second cohomology of the symplectic group explicit. To appear in Math. Zeit.. 12 pages