Genus-two Goeritz groups of lens spaces

Sangbum Cho

Vol. 265 (2013), No. 1, 1–16

DOI: 10.2140/pjm.2013.265.1

Abstract

Given a genus-g Heegaard splitting of a 3-manifold, the Goeritz group is defined to be the group of isotopy classes of orientation-preserving homeomorphisms of the manifold that preserve the splitting. In this work, we show that the Goeritz groups of genus-2 Heegaard splittings for lens spaces L(p,1) are finitely presented, and give explicit presentations of them.

Keywords

Heegaard splitting, Goeritz group, lens space, disk complex

Mathematical Subject Classification 2010

Primary: 57N10

Secondary: 57M60

Milestones

Received: 29 June 2012

Revised: 9 January 2013

Accepted: 4 February 2013

Published: 28 August 2013