Geodesic
Topological groups, $\mu$-types and their stabilizers
Journal of the European Mathematical Society, Tome 19 (2017) no. 10, pp. 2965-2995.

Voir la notice de l'article provenant de la source EMS Press

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, SGμ​(M)={pμ​:p∈SG​(M)} which is the quotient of the usual type space SG​(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 Stabμ(p), which is the stabilizer of pμ​. This group is nontrivial when p is unbounded in the sense of M; in fact it is a torsion-free solvable group.
DOI : 10.4171/jems/733
Classification : 03-XX
Keywords: o-minimality, definable groups, compactification 
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     title = {Topological groups, $\mu$-types and their stabilizers},
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Ya'acov Peterzil; Sergei Starchenko. Topological groups, $\mu$-types and their stabilizers. Journal of the European Mathematical Society, Tome 19 (2017) no. 10, pp. 2965-2995. doi : 10.4171/jems/733. http://geodesic.mathdoc.fr/articles/10.4171/jems/733/

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