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- Title
ON O-MINIMAL HOMOTOPY GROUPS.
- Authors
BARO, ELÍAS; OTERO, MARGARITA
- 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.
- Subjects
HOMOTOPY groups; HOMOTOPY theory; MATHEMATICAL analysis; EMBEDDING theorems; ALGEBRA
- Publication
Quarterly Journal of Mathematics, 2010, Vol 61, Issue 3, p275
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/hap011