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 , 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).
|Autori interni:||BERARDUCCI, ALESSANDRO|
|Autori:||BERARDUCCI A; PETERZIL YA'ACOV; PILLAY ANAND|
|Titolo:||Group covers, o-minimality, and categoricity|
|Anno del prodotto:||2010|
|Digital Object Identifier (DOI):||10.1142/S1793744210000259|
|Appare nelle tipologie:||1.1 Articolo in rivista|