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Category Archives: Uncategorized
Topologized Fundamental Groups: The Quotient Topology Part 1
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 compact-open topology, fundamental group, quasitopological fundamental group, quotient map, quotient topology, universal property of quotient maps
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How to “topologize” the fundamental group: a primer
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
The Griffiths twin cone and the harmonic archipelago have isomorphic fundamental group (Part 3)
We saw in the previous post that the problem of producing our isomorphism is solved provided we can produce a sufficiently large coherent collection of coi triples. But how is this to be accomplished? For example, given a (perhaps quite … Continue reading
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Wild Topology 