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SUMMARY:Van Kampen's Theorem: classic\, directed & generalized - Tobias He
 indel (University of Edinburgh)
DTSTART:20140227T140000Z
DTEND:20140227T150000Z
UID:TALK51168@talks.cam.ac.uk
CONTACT:Sean Moss
DESCRIPTION:The talk will start with a review of the basic definitions and
  main ideas of the Seifert-Van Kampen Theorem\, which states that the fund
 amental 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 es
 sentially the same proof. The situation is different for the so-called tau
 tological proof of the Van Kampen Theorem\, which relies on the equivalenc
 e between the fundamental groupoid π1(X) and the category of covering spa
 ces Cov(X) for any "nice" space X. The talk will describe the crucial poin
 ts of the tautological proof of the VK theorem and finishes with a discuss
 ion of its rôle in Brown's generalized Van Kampen theorems\, which gave r
 ise to the study of adhesive categories.\n
LOCATION:CMS\, MR13
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