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SUMMARY:Cobordisms of sutured manifolds - Andras Juhasz (Imperial)
DTSTART:20130211T140000Z
DTEND:20130211T150000Z
UID:TALK43230@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:Currently Heegaard Floer homology has two different extensions
  to\n3-manifolds with boundary: sutured Floer homology (SFH) for balanced\
 nsutured manifolds due to myself\, and the more recent bordered Floer\nhom
 ology for 3-manifolds with parametrized boundary due to Lipshitz\,\nOzsvat
 h\, and Thurston. In this talk\, I will introduce the notion of\ncobordism
  between sutured manifolds and explain how such cobordisms\ninduce maps on
  SFH. For this end\, I had to establish certain\nfunctoriality properties 
 of Heegaard Floer homology\, which then\nenabled me to fit the theory of S
 FH in a TQFT type framework.\n \nLipshitz et. al proved that bordered Floe
 r homology of a given\n3-manifold with parametrized boundary can be obtain
 ed from SFH and\nour cobordism maps. Another application is that we can de
 fine maps \ninduced on knot Floer homology by decorated knot coboridsms an
 d this\nyields a new invariant of surfaces embedded in 4-manifolds.\nSimil
 ar knot cobordism maps in the instanton setting were used by Kronheimer\na
 nd Mrowka to show that Khovanov homology detects the unknot.\n
LOCATION:CMS\, MR11
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