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University of Cambridge > Talks.cam > Differential Geometry and Topology Seminar > Knots, minimal surfaces and J-holomorphic curves

## Knots, minimal surfaces and J-holomorphic curvesAdd to your list(s) Download to your calendar using vCal - Joel Fine, Université Libre de Bruxelles
- Wednesday 26 January 2022, 16:00-17:00
- MR13.
If you have a question about this talk, please contact Henry Wilton. I will describe work in progress, parts of which are joint with 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 words the number of minimal surfaces doesn’t depend on the isotopy class of the link. These counts of minimal surfaces can be organised into a two-variable polynomial which is perhaps a known polynomial invariant of the link, such as HOMFLYPT . “Counting minimal surfaces” needs to be interpreted 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 of hyperbolic 4-space. This leads naturally to a new class of infinite-volume 6-dimensional symplectic manifolds with well behaved counts of J-holomorphic curves. This gives more potential knot invariants, for knots in 3-manifolds other than the 3-sphere. It also enables the counting of minimal surfaces in more general Riemannian 4-manifolds, besides hyperbolic space. This talk is part of the Differential Geometry and Topology Seminar series. ## This talk is included in these lists:- All CMS events
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