Mack, Thomas Patrick (2006) Quasiconvex subgroups and nets in hyperbolic groups. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-06052006-141903
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|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||12 May 2006|
|Non-Caltech Author Email:||tmack (AT) its.caltech.edu|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||05 Jun 2006|
|Last Modified:||26 Dec 2012 02:51|
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