Baro González, ElíasOtero, Margarita2023-06-202023-06-202010Baro E, Otero M. ON O-MINIMAL HOMOTOPY GROUPS. The Quarterly Journal of Mathematics 2010;61:275–89. https://doi.org/10.1093/qmath/hap011.0033-560610.1093/qmath/hap011https://hdl.handle.net/20.500.14352/42048We 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.engjournal articlehttps://doi.org/10.1093/qmath/hap011.http://qjmath.oxfordjournals.org/content/by/yearrestricted access512O-minimal homotopy groupsÁlgebra1201 Álgebra