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.

arXiv comment35 pages, to appear in Selecta Mathematica

References in corpus (8)

• The Picard group of the moduli space of curves with level structures
• The abelianization of the level 2 mapping class group
• Some finiteness results for groups of automorphisms of manifolds
• Torelli spaces of high-dimensional manifolds
• Mapping class groups of simply connected high-dimensional manifolds need not be arithmetic
• Rational Homological Stability for Automorphisms of Manifolds
• Characteristic numbers of manifold bundles over surfaces with highly connected fibers
• Some Hermitian K-groups via geometric topology

Cited by in corpus (10)

• The cohomology of Torelli groups is algebraic
• A homological approach to pseudoisotopy theory. I
• The mapping class group of connect sums of $S^2\times S^1$
• Mapping class groups of simply connected high-dimensional manifolds need not be arithmetic
• On the high-dimensional geography problem
• On characteristic classes of exotic manifold bundles
• 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