Geodesic
Topological groups, $\mu$-types and their stabilizers
Journal of the European Mathematical Society, Tome 19 (2017) no. 10, pp. 2965-2995 Cet article a éte moissonné depuis la source EMS Press

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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 
@article{JEMS_2017_19_10_a3,
     author = {Ya'acov Peterzil and Sergei Starchenko},
     title = {Topological groups, $\mu$-types and their stabilizers},
     journal = {Journal of the European Mathematical Society},
     pages = {2965--2995},
     year = {2017},
     volume = {19},
     number = {10},
     doi = {10.4171/jems/733},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/733/}
}
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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

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