Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777724 | Topology and its Applications | 2017 | 12 Pages |
Abstract
We generalize Brazas' topology on the fundamental group to the whole universal path space XË, i.e., to the set of homotopy classes of all based paths. We develop basic properties of the new notion and provide a complete comparison of the obtained topology with the established topologies, in particular with the Lasso topology and the CO topology, i.e., the topology that is induced by the compact-open topology. It turns out that the new topology is the finest topology contained in the CO topology, for which the action of the fundamental group on the universal path space is a continuous group action.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Žiga Virk, Andreas Zastrow,