Submission date: 25 March 2011.

Abstract:

We analyze groups definable in o-minimal structures as a combination of semi-linear groups and groups definable in o-minimal expansions of real closed fields. The analysis goes through their locally definable covers. We thus investigate locally definable abelian groups U in various settings and examine conditions under which the quotient of U by a discrete subgroup might be definable. This turns out to be related to the existence of the type-definable subgroup U^{00} and to the divisibility of U. As a corollary of the above analysis we prove the Compact Domination Conjecture in o-minimal expansions of ordered groups.

Mathematics Subject Classification: 03C64, 03C68, 22B99

Keywords and phrases: O-minimality, semi-bounded structures, locally definable groups, definable quotients, type-definable groups

Full text arXiv (1103.4770): pdf, ps.