Submission date: 8 February 2023

Abstract:

In this paper, we study the relation between the category of real Lie groups and that of groups definable in o-minimal expansions of the real field (which we will refer to as “definable groups”). It is known ([Pi88]) that any group definable in an o-minimal expansion of the real field is a Lie group, and in [COP] a complete characterization of when a Lie group has a “definable group” which is Lie isomorphic to it was given. In this paper we continue the analysis by explaining when a Lie homomorphism between definable groups is a definable isomorphism.

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Full text arXiv 2302.04251: pdf, ps.