The universal covering map in o-minimal expansions of groups

摘要

In this paper we study locally definable manifolds and we prove: (ⅰ) the existence of universal locally definable covering maps; (ⅱ) invariance results for locally definable covering maps, o-minimal fundamental groups and fundamental groupoids; (ⅲ) monodromy equivalence for locally constant o-minimal sheaves; (ⅳ) classification results for locally definable covering maps; (ⅴ) o-minimal Hurewicz and Seifert-van Kampen theorems.