Category Archives: Uncategorized

Topologized Fundamental Groups: The Quotient Topology Part 2 (Discreteness)

Posted on February 13, 2023 by Jeremy Brazas

In Part 1, I described the construction of , the fundamental group equipped with the quotient topology and some of the drama around failing to always be a topological group. In this second post, I plan to connect back to … Continue reading →

Posted in Fundamental group, Uncategorized | Tagged , , , | 4 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

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