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SUMMARY:The Fukaya-Morse algebra of a manifold - Jack Smith (UCL)
DTSTART:20171020T140000Z
DTEND:20171020T150000Z
UID:TALK89201@talks.cam.ac.uk
CONTACT:Nils Prigge
DESCRIPTION:Given a closed smooth manifold (and an appropriate Morse funct
 ion and metric) you can define the Morse cochain complex\, whose cohomolog
 y is isomorphic to that of the usual singular cochain complex.  You can al
 so define a product on the Morse complex\, which induces the familiar cup 
 product on cohomology\, but in general it fails to be associative at chain
  level and does not encode all of the structure contained in the singular 
 complex (e.g. Massey products).  I will describe how an idea of Fukaya lea
 ds naturally to the notion of an A-infinity algebra\, which is the correct
  weakening of the notion of associativity\, and a way to build the structu
 re of such an algebra on the Morse complex so that it captures (essentiall
 y) all of the information of the singular complex.  If time permits I will
  also discuss how to quantise (i.e. deform) this algebra in certain ways.
LOCATION:MR13
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