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.File in questo prodotto:
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