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SUMMARY:Annular Khovanov-Lee homology\, Braids\, and Cobordisms - Eli Grig
 sby\, Boston College
DTSTART:20170308T160000Z
DTEND:20170308T170000Z
UID:TALK69222@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION: Khovanov homology associates to a knot K in the three-sphere 
 a bigraded vector space arising as the homology groups of an abstract chai
 n complex. Using a deformation of Khovanov's complex\, due to Lee\, Rasmus
 sen defined an integer-valued knot invariant he called s(K) that gives a l
 ower bound on the 4-ball genus of knots\, sharp for knots that can be real
 ized as quasipositive braid closures.\n\nOn the other hand\, when K is a b
 raid closure\, its Khovanov complex can itself be realized in a natural wa
 y as a deformation of a triply-graded complex\, defined by Asaeda-Przytyck
 i-Sikora\, further studied by L. Roberts\, and now known as the (sutured) 
 annular Khovanov complex.\n\nIn this talk\, I will describe joint work wit
 h Tony Licata and Stephan Wehrli aimed at understanding an annular version
  of Lee's deformation of the Khovanov complex. In particular\, we obtain a
  family of real-valued braid conjugacy class invariants generalizing Rasmu
 ssen's "s" invariant that give bounds on the Euler characteristic of smoot
 hly-imbedded surfaces in the thickened solid torus as well as information 
 about the associated mapping class of the punctured disk. The algebraic mo
 del for this construction is the Upsilon invariant of Ozsvath-Stipsicz-Sza
 bo.
LOCATION:MR13
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