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Title page for ETD etd-07202007-144313


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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