Category Archives: Quasitopological groups

The “tau topology” on the fundamental group

Posted on November 9, 2024 by Jeremy Brazas

In the multipart series on topologies on fundamental groups, we’ve discussed the fundamental group with the quotient topology: . This is defined as having the quotient topology with respect to the map , that identifies homotopic loops. Here, is the … Continue reading →

Posted in Category Theory, coreflection functor, Fundamental group, Quasitopological groups, quasitopological groups, quotient topology, reflection functor, topological fundamental group, Topological groups, Uncategorized | Tagged , , , , , , | 1 Comment

Topologized Fundamental Groups: The Quotient Topology Part 4 (Subgroup Classifications)

Posted on October 7, 2023 by Jeremy Brazas

This is the last in a sequence of posts about the quotient topology. This one is about how the topological structure of can be used to classify certain generalizations of covering maps for locally complicated spaces. Sometimes it still amazes … Continue reading →

Posted in Algebraic Topology, core of a subgroup, Fundamental group, Generalized covering space theory, Griffiths twin cone, harmonic archipelago, Quasitopological groups, quotient topology, semicovering, topological fundamental group, Uncategorized | 7 Comments

Topologized Fundamental Groups: The Quotient Topology Part 1

Posted on August 25, 2022 by Jeremy Brazas

Next up for topologies on the fundamental group is what I’d consider the most “natural” one. It’s almost certainly the topology you’d most often get if you asked random topologists on the street to construct one for you. This is … Continue reading →

Posted in Algebraic Topology, compact-open topology, Fundamental group, Quasitopological groups, quotient topology, Topological groups, Uncategorized | Tagged , , , , , | 6 Comments