Real Algebraic and Analytic Geometry
e-mail: , ,
Submission: 2008, November 13.
It is known that a definably compact group G is an extension of a compact Lie group L by a divisible torsion-free normal subgroup. We show that the o-minimal higher homotopy groups of G are isomorphic to the corresponding higher homotopy groups of L. As a consequence, we obtain that all abelian definably compact groups of a given dimension are definably homotopy equivalent, and that their universal cover are contractible.
Mathematics Subject Classification (2000): 03C64, 57T20, 55P45.
Keywords and Phrases: definable group, Lie group, o-minimal homotopy.
Full text, 12p.: dvi 71k, ps.gz 169k, pdf 205k.