2008/10/02 by Elías Baro, Elias Baro, Baro, Elias +2
Computer Science · Mathematics · #03C64 #14P10 #55Q99 #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Topological and Geometric Data Analysis #math.LO #msc:03C64 #msc:14P10 #msc:55Q99
paper · pdf · doi:10.48550/arxiv.0810.0365
arxiv created 2008/10/02 · openalex publication_date 2008/10/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.