| Type of Document |
Dissertation |
| Author |
Mack, Thomas Patrick
|
| Author's Email Address |
tmack AT its.caltech.edu |
| URN |
etd-06052006-141903 |
| Persistent URL |
http://resolver.caltech.edu/CaltechETD:etd-06052006-141903 |
| Title |
Quasiconvex subgroups and nets in hyperbolic groups |
| Degree |
PhD |
| Option |
Mathematics |
| Advisory Committee |
| Advisor Name |
Title |
| Danny Calegari |
Committee Chair |
| Hee Oh |
Committee Member |
| Michael Aschbacher |
Committee Member |
| Nathan Dunfield |
Committee Member |
|
| Keywords |
- section
- quasiconvexity
- quasiconvex
- nets
- hyperbolic geometry
- finite automata
- cone type
|
| Date of Defense |
2006-05-12 |
| Availability |
unrestricted |
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.
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| Files |
| Filename |
Size |
Approximate Download Time
(Hours:Minutes:Seconds)
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| 28.8 Modem |
56K Modem |
ISDN (64 Kb) |
ISDN (128 Kb) |
Higher-speed Access |
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thesis.pdf |
315.79 Kb |
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00:00:45 |
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