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<title><string language="fre"><![CDATA[J. Fine - Knots, minimal surfaces and J-holomorphic curves]]></string></title>
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<string language="fre"><![CDATA[I
will describe work in progress, parts of which are joint with Marcelo 
Alves. Let L 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 L, and in this way obtain a knot 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 this 
“minimal surface polynomial" can be seen as a Gromov-Witten invariant 
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.]]></string></description>
<keyword><string language="fre"><![CDATA[Grenoble]]></string></keyword><keyword><string language="fre"><![CDATA[eem2021]]></string></keyword><keyword><string language="fre"><![CDATA[contraintes de courbures et espaces métriques]]></string></keyword><keyword><string language="fre"><![CDATA[curvature constraints and spaces of metrics]]></string></keyword><keyword><string language="fre"><![CDATA[knots]]></string></keyword><keyword><string language="fre"><![CDATA[minimal surfaces]]></string></keyword><keyword><string language="fre"><![CDATA[J-holomorphic curves]]></string></keyword>
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<date><dateTime>2021-07-02</dateTime></date>
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