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Journal of the London Mathematical Society 2002 65(2):257-270; doi:10.1112/S0024610701003015
© 2002 by London Mathematical Society
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© The London Mathematical Society

o-Minimal Fundamental Group, Homology and Manifolds

Alessandro Berarducci and Margarita Otero

Dipartimento di Matematica, Università a di Pisa Via Buonarroti 2, 56127 Pisa, Italy, berardu{at}dm.unipi.it
Dipartamento de Matemáticas, Universidad Autónoma de Madrid Cantoblanco, 28049 Madrid, Spain, margarita.otero{at}uam.es

Received 17 July 2000. Revision received 26 June 2001.

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.


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