Link homology theories from symplectic geometry

Details Link homology theories from symplectic geometry Link homology theories from symplectic geometry

2006-01-25

arxiv.org/abs/math/0601629v3

Mathematics

Symplectic Geometry

47 pages, 6 figures; revised version

Scientific paper

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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