Quasiconvex Subgroups and Nets in Hyperbolic Groups

Citation

Mack, Thomas Patrick (2006) Quasiconvex Subgroups and Nets in Hyperbolic Groups. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/35GG-W072. https://resolver.caltech.edu/CaltechETD:etd-06052006-141903

Abstract

Consider a hyperbolic group G and a quasiconvex subgroup H of G with [G:H] infinite. We construct a set-theoretic section s:G/H -> G of the quotient map (of sets) G -> G/H such that s(G/H) is a net in G; that is, any element of G is a bounded distance from s(G/H). This set arises naturally as a set of points minimizing word-length in each fixed coset gH. The left action of G on G/H induces an action on s(G/H), which we use to prove that H contains no infinite subgroups normal in G.

Item Type:	Thesis (Dissertation (Ph.D.))
Subject Keywords:	cone type; finite automata; hyperbolic geometry; nets; quasiconvex; quasiconvexity; section
Degree Grantor:	California Institute of Technology
Division:	Physics, Mathematics and Astronomy
Major Option:	Mathematics
Thesis Availability:	Public (worldwide access)
Research Advisor(s):	Calegari, Danny C.
Thesis Committee:	Calegari, Danny C. (chair) Oh, Hee Aschbacher, Michael Dunfield, Nathan M.
Defense Date:	12 May 2006
Record Number:	CaltechETD:etd-06052006-141903
Persistent URL:	https://resolver.caltech.edu/CaltechETD:etd-06052006-141903
DOI:	10.7907/35GG-W072
Default Usage Policy:	No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:	2461
Collection:	CaltechTHESIS
Deposited By:	Imported from ETD-db
Deposited On:	05 Jun 2006
Last Modified:	18 Dec 2020 19:15

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