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CATEGORIES:Junior Geometry Seminar
SUMMARY:The Fukaya-Morse algebra of a manifold - Jack Smit
h (UCL)
DTSTART;TZID=Europe/London:20171020T150000
DTEND;TZID=Europe/London:20171020T160000
UID:TALK89201AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/89201
DESCRIPTION:Given a closed smooth manifold (and an appropriate
Morse function and metric) you can define the Mor
se cochain complex\, whose cohomology is isomorphi
c to that of the usual singular cochain complex.
You can also define a product on the Morse complex
\, which induces the familiar cup product on cohom
ology\, but in general it fails to be associative
at chain level and does not encode all of the stru
cture contained in the singular complex (e.g. Mass
ey products). I will describe how an idea of Fuka
ya leads naturally to the notion of an A-infinity
algebra\, which is the correct weakening of the no
tion of associativity\, and a way to build the str
ucture of such an algebra on the Morse complex so
that it captures (essentially) all of the informat
ion of the singular complex. If time permits I wi
ll also discuss how to quantise (i.e. deform) this
algebra in certain ways.
LOCATION:MR13
CONTACT:Nils Prigge
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