Group covers, o-minimality, and categoricity
Confluentes Mathematici, Volume 2 (2010) no. 4, pp. 473-496.

We study the model theory of "covers" of groups H definable in an o-minimal structure M. We pose the question of whether any finite central extension G of H is interpretable in M, proving some cases (such as when H is abelian) as well as stating various equivalences. When M is an o-minimal expansion of the reals (so H is a definable Lie group) this is related to Milnor's conjecture [15], and many cases are known. We also prove a strong relative Lω1, ω-categoricity theorem for universal covers of definable Lie groups, and point out some notable differences with the case of covers of complex algebraic groups (studied by Zilber and his students).

Published online:
DOI: 10.1142/S1793744210000259
Alessandro Berarducci 1; Ya’acov Peterzil 1; Anand Pillay 1

1
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Alessandro Berarducci; Ya’acov Peterzil; Anand Pillay. Group covers, $o$-minimality, and categoricity. Confluentes Mathematici, Volume 2 (2010) no. 4, pp. 473-496. doi : 10.1142/S1793744210000259. https://cml.centre-mersenne.org/articles/10.1142/S1793744210000259/

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