English

Describing elements of the genus-2 Goeritz group of $S^3$

Geometric Topology 2019-12-20 v1

Abstract

In this article we present a finite generating set G2G_2 of H2\mathcal{H}_2, the genus-2 Goeritz group of S3S^3, in terms of Dehn twists about certain simple closed curves on the standard Heegaard surface. We present an algorithm that describes an element ψH2\psi\in\mathcal{H}_2 as a word in the alphabet of G2G_2 in a certain format. Using a complexity measure defined on reducing spheres, we show that such a description of ψ\psi is unique.

Keywords

Cite

@article{arxiv.1912.08894,
  title  = {Describing elements of the genus-2 Goeritz group of $S^3$},
  author = {Sreekrishna Palaparthi and Swapnendu Panda},
  journal= {arXiv preprint arXiv:1912.08894},
  year   = {2019}
}