Homotopy theory provides a framework for classifying spaces up to continuous deformations, and its application to gauge groups has been instrumental in advancing our understanding of the topological ...

Given a collection {πn:n = 1, 2, ⋯} of countable groups such that πi is abelian and admits π1 as a group of operators for i ≥ 2, we construct here an arcwise connected compact metric space of trivial ...

Elements λn, n ≥ 0, which generate the homotopy groups of spheres in the category of simplicial Lie algebras are shown to have Hopf invariant one. This fact is shown to have strong implications for ...