Describing elements of the genus-2 Goeritz group of S³

2019/12/18 by Palaparthi, Sreekrishna, Panda, Swapnendu
#57N12 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1912.08894

Abstract

In this article we present a finite generating set G₂ of H₂, the genus-2 Goeritz group of S³, in terms of Dehn twists about certain simple closed curves on the standard Heegaard surface. We present an algorithm that describes an element ψ\inH₂ as a word in the alphabet of G₂ in a certain format. Using a complexity measure defined on reducing spheres, we show that such a description of ψ is unique.

Related

• Reducing spheres of genus-2 Heegaard splitting of S³
• Generating the genus g+1 Goeritz group of a genus g handlebody
• Genus 2 Goeritz Equivalence in S³
• Powell's Conjecture on the Goeritz group of S³ is stably true
• The genus two Goeritz group of S² × S¹