Comparison of Topologies on Homotopy Groups with Subgroup Topology Viewpoint
Naghme Shahami, Behrooz Mashayekhy

TL;DR
This paper reviews and compares different topologies on homotopy groups of topological spaces, focusing on subgroup topology, to enhance understanding and utility in algebraic topology.
Contribution
It introduces a comparison framework for various topologies on homotopy groups using subgroup topology, providing new insights into their relationships.
Findings
Comparison of known topologies on homotopy groups
Results on topologized homotopy groups using subgroup topology
Enhanced understanding of algebraic topology structures
Abstract
By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies on homotopy groups. Then by reviewing some famous subgroups of homotopy groups and using the concept of subgroup topology, we intend to compare these topologies in order to present some results on topologized homotopy groups.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Fuzzy and Soft Set Theory · Topological and Geometric Data Analysis
