Tag Archives: fundamental group

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 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

How to “topologize” the fundamental group: a primer

Posted on April 26, 2022 by Jeremy Brazas

The fundamental group, from algebraic topology, is one of the most widely used invariants in mathematics. Topological groups, such as pro-finite groups, Lie groups, ordered groups, etc, also arise in many different areas. So it’s natural to ask, can the … Continue reading →

Posted in Algebraic Topology, Fundamental group, Topological groups, Uncategorized | Tagged , , , , | 5 Comments