| 21. | These well understood elements account for most elements of the stable homotopy groups of spheres in small dimensions.
|
| 22. | Stephen Smale expressed the regular homotopy classes of immersions as the homotopy groups of a certain Stiefel manifold.
|
| 23. | They can be used to construct the Greek letter infinite families in the stable homotopy groups of spheres.
|
| 24. | Hurewicz theorem ), then the nonabelian cohomology may be thought of as a dual of homotopy groups.
|
| 25. | Topological spaces with differing homotopy groups are never equivalent ( homeomorphic ), but the converse is not true.
|
| 26. | These are related to relative homotopy groups and to " n "-adic homotopy groups respectively.
|
| 27. | These are related to relative homotopy groups and to " n "-adic homotopy groups respectively.
|
| 28. | Like the fundamental group or the higher homotopy groups of a space, homology groups are important topological invariants.
|
| 29. | One of the most important problems in stable homotopy theory is the computation of stable homotopy groups of spheres.
|
| 30. | In some cases it can be shown that the higher homotopy groups of " Y " are trivial.
|
