The definable fundamental group of a definable set in an o-minimal expansion of a field is computed. This is achieved by proving the relevant case of the o-minimal van Kampen theorem. This result is applied to show that if the geometrical realization of a simplicial complex over an o-minimal expansion of a field is a definable manifold of dimension not 4, then its geometrical realization over the reals is a topological manifold.

o-Minimal Fundamental Group, Homology and Manifolds

BERARDUCCI, ALESSANDRO;
2002-01-01

Abstract

The definable fundamental group of a definable set in an o-minimal expansion of a field is computed. This is achieved by proving the relevant case of the o-minimal van Kampen theorem. This result is applied to show that if the geometrical realization of a simplicial complex over an o-minimal expansion of a field is a definable manifold of dimension not 4, then its geometrical realization over the reals is a topological manifold.
2002
Berarducci, Alessandro; Otero, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/69873
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