11. Hence the only non-trivial homotopy group is \ pi _ 1 ( X) 12. A continuous map between two topological spaces induces a group homomorphism between the associated homotopy groups . 13. This property makes fibrant objects the " correct " objects on which to define homotopy groups . 14. Another way is to examine the type of topological singularity at a point with the homotopy group . 15. For stable homotopy groups there are more precise results about " p "-torsion. 16. On homotopy groups , where ? denotes the loop functor and'" denotes the smash product. 17. In the two examples above all the maps between homotopy groups are applications of the suspension functor. 18. As the third homotopy group of S ^ 3 has been found to be the set of integers, 19. The stable homotopy groups form the coefficient ring of an extraordinary cohomology theory, called stable cohomotopy theory. 20. It therefore came as a great surprise historically that the corresponding homotopy groups are not trivial in general.
