A new topology on the universal path space

Žiga Virk , Andreas Zastrow

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.
Author Žiga Virk
Žiga Virk,,
-
, Andreas Zastrow IM
Andreas Zastrow,,
- Institute of Mathematics
Other language title versions
Journal seriesTopology and Its Applications, ISSN 0166-8641
Issue year2017
Vol231
Pages186-196
Publication size in sheets0.5
Keywords in Englishtopology on the fundamental group, topology on the path space, quasi topological fundamental group, compact open topology
DOIDOI:10.1016/j.topol.2017.09.015
URL https://doi.org/10.1016/j.topol.2017.09.015
Languageen angielski
Score (nominal)20
ScoreMinisterial score = 20.0, 20-12-2017, ArticleFromJournal
Ministerial score (2013-2016) = 20.0, 20-12-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 0.377 (2) - 2016=0.464 (5)
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