On the mapping class groups of #r(Sp × Sp) for p = 3, 7

Abstract

For Mr := #r(Sp × Sp) for p = 3, 7, we calculate π0Diff(Mr/ Θ2p+1 and ε(Mr, respectively the group of isotopy classes of orientation preserving diffeomorphisms of Mr modulo isotopy classes with representatives which are the identity outside a 2p-disc and the group of homotopy classes of orientation preserving homotopy equivalences of Mr. © 2010 Springer-Verlag.