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The Quarterly Journal of Mathematics Advance Access published online on March 17, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/hap011
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

ON O-MINIMAL HOMOTOPY GROUPS

Elías Baro{dagger} and Margarita Otero {ddagger}

Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain

{dagger} Corresponding author. E-mail: elias.baro{at}uam.es

Received 15 August 2008; revised 28 January 2009
  Abstract

We work over an o-minimal expansion of a real closed field. The o-minimal homotopy groups of a definable set are defined naturally using definable continuous maps. We prove that any two semialgebraic maps which are definably homotopic are also semialgebraically homotopic. This result together with known results on semialgebraic homotopy allows us to develop an o-minimal homotopy theory. In particular, we obtain o-minimal versions of the Hurewicz theorems and the Whitehead theorem.

{ddagger} E-mail: margarita.otero{at}uam.es


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