On o-minimal homotopy groups

Details On o-minimal homotopy groups On o-minimal homotopy groups

2008-10-02

arxiv.org/abs/0810.0365v1

Mathematics

Logic

Scientific paper

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 the study of semialgebraic homotopy done by H. Delfs and M. Knebusch allows us to develop an o-minimal homotopy theory. In particular, we obtain o-minimal versions of the Hurewicz theorems and the Whitehead theorem.

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