Heegaard Floer homology of (n,n)-torus links: computations and questions

Abstract

In this article we study the Heegaard Floer link homology of $(n, n)$-torus links. The Alexander multigradings which support non-trivial homology form a string of $n-1$ unit hypercubes in $\mathbb{R}^{n}$, and we compute the ranks and gradings of the homology in nearly all Alexander gradings. We also conjecture a complete description of the link homology and provide some support for this conjecture. This article is taken from the author's 2007 Ph.D. thesis and contains several open questions.