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Preprint Number 775

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775. Ya'acov Peterzil and Sergei Starchenko
Topological groups, μ-types and their stabilizers
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Submission date: 18 September 2014.

Abstract:

We consider an arbitrary topological group G definable in a structure M, such that some basis for the topology of G consists of sets definable in M.
To each such group G we associate a compact G-space of partial types S^μ_G(M)={p_μ : p in S_G(M)} which is the quotient of the usual type space S_G(M) by the relation of two types being “infinitesimally close to each other”. In the o-minimal setting, if p is a definable type then it has a corresponding definable subgroup Stab_μ(p), which is the stabilizer of p_μ. This group is nontrivial when p is unbounded in the sense of M; in fact it is a torsion-free solvable group.
Along the way, we analyze the general construction of S^μ_G(M) and its connection to the Samuel compactification of topological groups.

Mathematics Subject Classification: 03C64, 03C98

Keywords and phrases: O-minimality, definable groups, compactification

Full text arXiv 1409.5355: pdf, ps.


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