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

Abstract

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

35 pages, to appear in Selecta Mathematica

References in corpus (2)

• Mapping class groups of simply connected high-dimensional manifolds need not be arithmetic
• Some Hermitian K-groups via geometric topology

Cited by in corpus (9)

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• A homological approach to pseudoisotopy theory. I
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• Mapping class groups of simply connected high-dimensional manifolds need not be arithmetic
• The mapping class group of connect sums of $S^2\times S^1$
• On automorphisms of high-dimensional solid tori
• Mapping class group of manifolds which look like $3$-dimensional complete intersections
• A note on rational homological stability for automorphisms of manifolds
• Some Hermitian K-groups via geometric topology