Topological groups, μ-types and their stabilizers

Ya'Acov Peterzil, Sergei Starchenko

Research output: Contribution to journalArticlepeer-review


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, SμG.(M) = {pμ : p ϵ 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 fact, it is a torsion-free solvable group. Along the way, we analyze the general construction of SμG.(M) and its connection to the Samuel compactification of topological groups.

Original languageEnglish
Pages (from-to)2965-2995
Number of pages31
JournalJournal of the European Mathematical Society
Issue number10
StatePublished - 2017

Bibliographical note

Funding Information:
The authors thank the US-Israel Binational Science Foundation for its support, and also thank the Mathematical Science Research Institute at Berkeley for its hospitality during Spring 2014. The second author thanks the National Science Foundation for support.


  • Compactification
  • Definable groups
  • O-minimality

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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