Article ID Journal Published Year Pages File Type
5777724 Topology and its Applications 2017 12 Pages PDF
Abstract
We generalize Brazas' topology on the fundamental group to the whole universal path space X˜, 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.
Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology
Authors
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