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Quasiconvex Subgroups and Nets in Hyperbolic Groups


Mack, Thomas Patrick (2006) Quasiconvex Subgroups and Nets in Hyperbolic Groups. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/35GG-W072.


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:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2461
Deposited By: Imported from ETD-db
Deposited On:05 Jun 2006
Last Modified:18 Dec 2020 19:15

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