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On o-minimal homotopy groups Baro González, Elías Otero, Margarita 512 O-minimal homotopy groups Álgebra 1201 Álgebra 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. GEOR Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T00:07:59Z 2023-06-20T00:07:59Z 2010 journal article https://hdl.handle.net/20.500.14352/42048 0033-5606 10.1093/qmath/hap011 eng info:eu-repo/grantAgreement/MICINN//MTM2008-00272/ES/GEOMETRIA REAL/ Grupos UCM 910444 Baro E, Otero M. ON O-MINIMAL HOMOTOPY GROUPS. The Quarterly Journal of Mathematics 2010;61:275–89. https://doi.org/10.1093/qmath/hap011. restricted access application/pdf Oxford University Press