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SUMMARY:Knots\, minimal surfaces and J-holomorphic curves - Joel Fine\, Un
 iversité Libre de Bruxelles
DTSTART:20220126T160000Z
DTEND:20220126T170000Z
UID:TALK167468@talks.cam.ac.uk
CONTACT:Henry Wilton
DESCRIPTION:I will describe work in progress\, parts of which are joint wi
 th Marcelo Alves. Let K be a knot or link in the 3-sphere. I will explain 
 how one can count minimal surfaces in hyperbolic 4-space which have ideal 
 boundary equal to K\, and in this way obtain a link invariant. In other wo
 rds the number of minimal surfaces doesn’t depend on the isotopy class o
 f the link. These counts of minimal surfaces can be organised into a two-v
 ariable polynomial which is perhaps a known polynomial invariant of the li
 nk\, such as HOMFLYPT .\n\n“Counting minimal surfaces” needs to be int
 erpreted carefully here\, similar to how Gromov-Witten invariants “count
 ” J-holomorphic curves. Indeed I will explain how these minimal surface 
 invariants can be seen as Gromov-Witten invariants for the twistor space o
 f hyperbolic 4-space. This leads naturally to a new class of infinite-volu
 me 6-dimensional symplectic manifolds with well behaved counts of J-holomo
 rphic curves. This gives more potential knot invariants\, for knots in 3-m
 anifolds other than the 3-sphere. It also enables the counting of minimal 
 surfaces in more general Riemannian 4-manifolds\, besides hyperbolic space
 .
LOCATION:MR13
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