The geometry of the handlebody groups I: Distortion

2011/01/10 by Ursula Hamenstädt, Sebastian Hensel, Hamenstädt, Ursula +1
Mathematics · #20E36 #57M99 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Metric Geometry (math.MG) #math.GR #math.GT #math.MG #msc:20E36 #msc:57M99

paper · pdf · doi:10.48550/arxiv.1101.1838

31 pages, 3 figures

arxiv created 2011/04/12 · arxiv updated 2015/03/17

Abstract

We show that the mapping class group of a handlebody of genus at least 2 (with any number of marked points or spots) is exponentially distorted in the mapping class group of its boundary surface. The same holds true for solid tori with at least two marked points or spots.

Related

• On the Mapping class group of a genus 2 handlebody
• A lower bound of the distortion of the Torelli group in the mapping class group with boundary components
• A simple presentation of the handlebody group of genus 2
• A Complex of Incompressible Surfaces for handlebodies and the Mapping Class Group
• A twisted first homology group of the handlebody mapping class group