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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Knot contact homology and topological strings - To
bias Ekholm\, Uppsala
DTSTART;TZID=Europe/London:20131127T160000
DTEND;TZID=Europe/London:20131127T170000
UID:TALK46741AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/46741
DESCRIPTION:We discuss relations between open topological stri
ngs and Chern-Simons theory and contact homology i
n the context of knot invariants. The starting poi
nt on the physics side is the relation between the
HOMFLY polynomial and open topological strings (o
pen Gromov-Witten invariants) in the cotangent bun
dle of the three-sphere\, and (after large N trans
ition) in the total space of the sum of two (-1)-l
ine bundles over the projective line. The starting
point on the geometry side is to apply contact h
omology\, a theory of Floer homological nature for
contact rather than symplectic manifolds\, to the
co-normal lift of a knot\, which is a Legendrian
torus in the unit cotangent bundle of the three-sp
here with contact form the action form. The physic
s setup leads to a polynomial knot invariant (a Q-
deformation of the A-polynomial) and the geometry
setup leads to another polynomial knot invariant\,
the so called augmentation polynomial. It was rec
ently observed that these two polynomial knot inva
riants seem to agree and we will discuss the under
lying reason. This polynomial\, conjecturally\, a
lso encodes data for the B-model mirror of the A-m
odel theory mentioned above. If time permits we wi
ll also discuss the case of many component links w
here the corresponding mirror theory is a more inv
olved higher dimensional theory involving a co-iso
troppic brane. The talk is based on joint work wi
th Aganagic\, Ng\, and Vafa.
LOCATION:MR13
CONTACT:Ivan Smith
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