Comparison of Topologies on Fundamental Groups with Subgroup Topology Viewpoint

Abstract

In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the 21st century onwards. In this paper by reviewing these topologies, using the concept of subgroup topology, we are going to compare these topologies in order to present some results on topologized fundamental groups.

arXiv comment23 pages

References in corpus (5)

• The fundamental group as a topological group
• The topological fundamental group and free topological groups
• Topological fundamental groups and small generated coverings
• Spanier spaces and covering theory of non-homotopically path Hausdorff spaces
• A natural pseudometric on homotopy groups of metric spaces