Besides the work on the homotopy groups of spheres and related spaces, he did important work on Hopkins and Smith.
42.
A higher homotopy van Kampen theorem then enables one to derive some new information on homotopy groups and even on homotopy types.
43.
These groups are actually the homotopy groups of an object corresponding to " X " in the stable homotopy category.
44.
However, despite intense research in calculating the homotopy groups of spheres, even in two dimensions a complete list is not known.
45.
In condensed matter physics, the theory of homotopy groups provides a natural setting for description and classification of defects in ordered systems.
46.
The path component group can also be characterized as the zeroth homotopy group, \ pi _ 0 ( G, e ).
47.
This period of his work culminated in his book " Composition methods in homotopy groups of spheres " ( 1962 ).
48.
I'm pretty sure that I need to consider a sequence of homotopy groups, but I'm not entirely sure.
49.
This is done by constructing short exact sequences starting with an Eilenberg & ndash; MacLane space for the homotopy group to be removed.
50.
For some spaces, such as tori, all higher homotopy groups ( that is, second and higher homotopy groups ) are trivial.
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