University of Cambridge > > Junior Category Theory Seminar > Van Kampen's Theorem: classic, directed & generalized

Van Kampen's Theorem: classic, directed & generalized

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  • UserTobias Heindel (University of Edinburgh)
  • ClockThursday 27 February 2014, 14:00-15:00
  • HouseCMS, MR13.

If you have a question about this talk, please contact Sean Moss.

The talk will start with a review of the basic definitions and main ideas of the Seifert-Van Kampen Theorem, which states that the fundamental group(oid) functor preserves certain colimits from the category of “nice” topological spaces to the category of group(oid)s. It is much less well-known that the theorem can be generalized without much complication to directed topological spaces and their fundamental categories, using essentially the same proof. The situation is different for the so-called tautological proof of the Van Kampen Theorem, which relies on the equivalence between the fundamental groupoid π1(X) and the category of covering spaces Cov(X) for any “nice” space X. The talk will describe the crucial points of the tautological proof of the VK theorem and finishes with a discussion of its rôle in Brown’s generalized Van Kampen theorems, which gave rise to the study of adhesive categories.

This talk is part of the Junior Category Theory Seminar series.

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