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o-MINIMAL FUNDAMENTAL GROUP, HOMOLOGY AND MANIFOLDS

Published online by Cambridge University Press:  24 March 2003

ALESSANDRO BERARDUCCI  and
MARGARITA OTERO
ALESSANDRO BERARDUCCI
Affiliation:
Dipartimento di Matematica, Università a di Pisa, Via Buonarroti 2, 56127 Pisa, Italy; [email protected]
MARGARITA OTERO
Affiliation:
Dipartamento de Matemáticas, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain; [email protected]
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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.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 2 , April 2002 , pp. 257 - 270
Copyright
The London Mathematical Society, 2002

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