EleftheriouP072007.pdf (499.92 kB)
Groups definable in linear o-minimal structures
thesis
posted on 2007-07-20, 00:00 authored by Pantelis E. EleftheriouLet 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.
History
Date Modified
2017-06-05Defense Date
2007-06-29Research Director(s)
Sergei StarchenkoCommittee Members
Lou van den Dries Steven Buechler Gregory Madey Julia KnightDegree
- Doctor of Philosophy
Degree Level
- Doctoral Dissertation
Language
- English
Alternate Identifier
etd-07202007-144313Publisher
University of Notre DameProgram Name
- Mathematics
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