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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 Ο€1(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 rΓ΄le 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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