Category Archives: Uncategorized

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

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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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Spanier Groups: a modern take on vintage covering space theory

Edwin H. Spanier’s 1966 Algebraic Topology book is a true classic. Well-written and precise, I still find myself referring to it regularly even though it is really “old.” Spanier takes a unique approach to covering space theory that I haven’t … Continue reading

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