arXiv subjects

Naghme Shahami

Publications and source records attributed to Naghme Shahami.

3 recordsLinked to original sources

arXiv2026

Comparison of Topologies on Homotopy Groups with Subgroup Topology Viewpoint

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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arXiv2026

Covering Maps with respect to Topologies on the Fundamental Group

In this paper, using the classical covering theory, we introduce a generalization of covering maps of a space $X$ with respect to a topology $\tau$ on the fundamental group of $X$. We show that the famous notions, covering, semicovering, generalized covering and fibration maps are of special cases of this new notion $\pi_1^{\tau}$-covering map. Moreover, among presenting some properties for this new notion, we compare $\pi_1^{\tau}$-covering maps of a space $X$ for several famous topologies on the fundamental group of $X$.

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arXiv2025

Comparison of Topologies on Fundamental Groups with Subgroup Topology Viewpoint

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.

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