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

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arxiv 1902.10097 v2 pith:LWVNSSXV submitted 2019-02-26 math.AT math.GT

Manuel Krannich This is my paper · ORCID
classification math.ATmath.GT
keywords groupmanifoldsclasshomotopymappingabelianisationsautomorphismcompute
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abstract

We compute the mapping class group of the manifolds $\sharp^g(S^{2k+1}\times S^{2k+1})$ 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.

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  1. The cohomology of Torelli groups is algebraic

    math.AT 2019-08 accept novelty 7.0 of 10

    For 2n ≥ 6 and g ≥ 2, the rational cohomology of the Torelli group of W_g = #^g S^n × S^n is an algebraic representation of Sp_{2g} or O_{g,g}, and its classifying space is nilpotent.

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