Real Algebraic and Analytic Geometry

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258. Elías Baro, Margarita Otero:
On o-minimal homotopy groups.

e-mail: ,

Submission: 2008, August 29.

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.

Mathematics Subject Classification (2000): 03C64, 14P10, 55Q99.

Full text, 17p.: dvi 86k, ps.gz 183k, pdf 241k.

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