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Link homology theories from symplectic geometry

Ciprian Manolescu
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Abstract

For each positive integer n, Khovanov and Rozansky constructed an invariant of links in the form of a doubly-graded cohomology theory whose Euler characteristic is the sl(n) link polynomial. We use Lagrangian Floer cohomology on some suitable affine varieties to build a similar series of link invariants, and we conjecture them to be equal to those of Khovanov and Rozansky after a collapsation of the bigrading. Our work is a generalization of that of Seidel and Smith, who treated the case n=2.

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Ciprian Manolescu. 2006-09-12. Link homology theories from symplectic geometry. https://arxiv.org/abs/math/0601629

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