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SUMMARY:Knot contact homology and topological strings - Tobias Ekholm\, Up
 psala
DTSTART:20131127T160000Z
DTEND:20131127T170000Z
UID:TALK46741@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:We discuss relations between open topological strings and Cher
 n-Simons theory and contact homology in the context of knot invariants. Th
 e starting point on the physics side is the relation between the HOMFLY po
 lynomial and open topological strings (open Gromov-Witten invariants) in t
 he cotangent bundle of the three-sphere\, and (after large N transition) i
 n the total space of the sum of two (-1)-line bundles over the projective 
 line. The starting point  on the geometry side is to apply contact homolog
 y\, a theory of Floer homological nature for contact rather than symplecti
 c manifolds\, to the co-normal lift of a knot\, which is a Legendrian toru
 s in the unit cotangent bundle of the three-sphere with contact form the a
 ction form. The physics setup leads to a polynomial knot invariant (a Q-de
 formation of the A-polynomial) and the geometry setup leads to another pol
 ynomial knot invariant\, the so called augmentation polynomial. It was rec
 ently observed that these two polynomial knot invariants seem to agree and
  we will discuss the underlying reason.  This polynomial\, conjecturally\,
  also encodes data for the B-model mirror of the A-model theory mentioned 
 above. If time permits we will also discuss the case of many component lin
 ks where the corresponding mirror theory is a more involved higher dimensi
 onal theory involving a co-isotroppic brane.  The talk is based on joint w
 ork with Aganagic\, Ng\, and Vafa.
LOCATION:MR13
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