A twisted first homology group of the Goeritz group of 3-sphere

Abstract

Given a genus-g Heegaard splitting of a 3-sphere, the genus-g Goeritz group is defined to be the group of the isotopy classes of orientation preserving homeomorphism of the 3-sphere that preserve the splitting. In this paper, we determine the twisted first (co)homology group of the genus-2 Goeritz group of 3-sphere.

12 pages, 3 figures

References in corpus (2)

• The genus two Goeritz group of $S^2\times S^1$
• A twisted first homology group of the handlebody mapping class group