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

preprint2011arXivOpen access

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 MrM_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.

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