On the mapping class groups of $#_r(S^p \times S^p)$ for $p = 3, 7$
Geometric Topology
2011-10-31 v2
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 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.
Cite
@article{arxiv.0905.0423,
title = {On the mapping class groups of $#_r(S^p \times S^p)$ for $p = 3, 7$},
author = {Diarmuid Crowley},
journal= {arXiv preprint arXiv:0905.0423},
year = {2011}
}
Comments
Presentation 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