A new topology on the universal path space

Žiga Virk , Andreas Zastrow


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.
Author Žiga Virk
Žiga Virk,,
, Andreas Zastrow (FMPI / IM)
Andreas Zastrow,,
- Institute of Mathematics
Other language title versions
Journal seriesTopology and Its Applications, ISSN 0166-8641, (A 20 pkt)
Issue year2017
Publication size in sheets0.5
Keywords in Englishtopology on the fundamental group, topology on the path space, quasi topological fundamental group, compact open topology
ASJC Classification2608 Geometry and Topology
URL https://doi.org/10.1016/j.topol.2017.09.015
Languageen angielski
Score (nominal)20
Score sourcejournalList
ScoreMinisterial score = 20.0, 28-01-2020, ArticleFromJournal
Publication indicators WoS Citations = 1; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 1.051; WoS Impact Factor: 2017 = 0.549 (2) - 2017=0.579 (5)
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