Pseudoholomorphic quilts and Khovanov homology

Details Pseudoholomorphic quilts and Khovanov homology Pseudoholomorphic quilts and Khovanov homology

2009-12-03

arxiv.org/abs/0912.0669v2

Mathematics

Symplectic Geometry

Introduction expanded, an issue with signs removed, various minor edits

Scientific paper

We further study the symplectic Khovanov homology of Seidel and Smith and its generalization to even tangles. We associate homomorphisms to elementary (as well as minimal) cobordisms between tangles. We define the symplectic analogues $H_s^m$ of Khovanov's arc algebras and equip the invariant assigned to an $(m,n)$-tangle with the structure of an $(H_s^m, H_s^n)$-bimodule. We show that $H_s^m$ and Khovanov's $H^m$ are isomorphic as algebras over $\Z/2$. We also obtain an exact triangle for the Seidel-Smith invariant similar to that of Khovanov homology.

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