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SUMMARY:The Tangent Bundle of a Microlinear Space - Filip Bár (University
  of Cambridge)
DTSTART:20120307T160000Z
DTEND:20120307T170000Z
UID:TALK36908@talks.cam.ac.uk
CONTACT:Filip Bár
DESCRIPTION:We prove a characterization of quasi colimits\, namely that an
 y cone of Weil algebras is a quasi colimit iff R perceives it as a limit (
 in our smooth universe of sets). This result is of both theoretical and pr
 actical relevance. Geometrically it implies that tangent bundle constructi
 ons on R\, for example\, the fiberwise addition of tangent vectors\, are u
 niversal. Because of this the construction can be transferred to any space
  that perceives quasi colimits as limits\, i.e.\, it works for the tangent
  bundle of any _microlinear space_. In fact\, any such tangent bundle turn
 s out to be a K-L vector bundle. (This means that any fiber is a K-L R-mod
 ule.)\n\nThis talk will cover the sections 2.3.2\, 3.1\, 3.2.1 of Lavendho
 mme's book.
LOCATION:Centre for Mathematical Sciences\, MR4
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