Topological groups, -types and their stabilizers
Ya'acov Peterzil
University of Haifa, IsraelSergei Starchenko
University of Notre Dame, USA
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Abstract
We consider an arbitrary topological group definable in a structure , such that some basis for the topology of consists of sets definable in . To each such group we associate a compact -space of partial types, which is the quotient of the usual type space by the relation of two types being "infinitesimally close to each other". In the o-minimal setting, if is a definable type then it has a corresponding definable subgroup Stab, which is the stabilizer of . This group is nontrivial when is unbounded in the sense of ; in fact it is a torsion-free solvable group.
Along the way, we analyze the general construction of and its connection to the Samuel compactification of topological groups.
Cite this article
Ya'acov Peterzil, Sergei Starchenko, Topological groups, -types and their stabilizers. J. Eur. Math. Soc. 19 (2017), no. 10, pp. 2965–2995
DOI 10.4171/JEMS/733