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A twisted first homology group of the handlebody mapping class group

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arxiv 1502.07048 v1 pith:XEFUAFME submitted 2015-02-25 math.GT math.ATmath.GR

Tomohiko Ishida , Masatoshi Sato This is my paper · ORCID
classification math.GTmath.ATmath.GR
keywords groupfirsthomologyclasshandlebodymappingtwistedboundary
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abstract

Let $H_{g}$ be a 3-dimensional handlebody of genus $g$. We determine the twisted first homology group of the mapping class group of $H_{g}$ with coefficients in the first integral homology group of the boundary surface $\partial H_{g}$ for $g\geq 2$.

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  1. Abelianizations of finite-index subgroups of the handlebody group

    math.GT 2026-07 accept novelty 6.0 of 10

    For genus ≥ 4, meridian multitwists vanish in H_1 of any finite-index subgroup of the handlebody group, and subgroups containing the Torelli group, twist group, or Johnson kernel have trivial rational abelianization.

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