A twisted first homology group of the handlebody mapping class group

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 $g\ge 2$.

arXiv comment27 pages, 4 figures

References in corpus (5)

• Stabilization for mapping class groups of 3-manifolds
• Cohomological Aspects of Magnus Expansions
• The first homology group of the mapping class group of a nonorientable surface with twisted coefficients
• A simple presentation of the handlebody group of genus 2
• The 2-torsion in the second homology of the genus $3$ mapping class group

Cited by in corpus (2)

• Generalized Long-Moody functors
• A twisted first homology group of the Goeritz group of 3-sphere