| Type of Document |
Dissertation |
| Author |
Eleftheriou, Pantelis E.
|
| Author's Email Address |
pelefthe@nd.edu |
| URN |
etd-07202007-144313 |
| Title |
Groups definable in linear o-minimal structures |
| Degree |
Doctor of Philosophy |
| Department |
Mathematics |
| Advisory Committee |
| Advisor Name |
Title |
| Gregory Madey |
Committee Chair |
| Julia Knight |
Committee Member |
| Lou van den Dries |
Committee Member |
| Sergei Starchenko |
Committee Member |
| Steven Buechler |
Committee Member |
|
| Keywords |
- groups
- o-minimal structures
|
| Date of Defense |
2007-06-29 |
| Availability |
unrestricted |
Abstract
Let M = be a linear o-minimal expansion of an ordered group, and G an n-dimensional group definable in M. We show that if G is definably connected with respect to the t-topology, then it is definably isomorphic to a definable quotient group U/L, for some convex V-definable subgroup U of and a lattice L of rank equal to the dimension of the 'compact part' of G. This is suggested as a structure theorem analogous to the classical theorem that every connected abelian Lie group is Lie isomorphic to a direct sum of copies of the additive group of the reals and the circle topological group S^1. We then apply our analysis and prove Pillay's Conjecture and
the Compact Domination Conjecture for a saturated M as above. En route, we show that the o-minimal fundamental group of G is isomorphic to L. Finally, we state some restrictions on L.
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| Filename |
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EleftheriouP072007.pdf |
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