We show that the knot lattice homology of a knot in an L-space is chain homotopy equivalent to the knot Floer homology of the same knot (viewed these invariants as filtered chain complexes over the polynomial ring Z/2Z[U]). Suppose that G is a negative definite plumbing tree which contains a vertex w such that G-w is a union of rational graphs. Using the identification of knot homologies we show that for such graphs the lattice homology HF-(G) is isomorphic to the Heegaard Floer homology HF-(YG) of the corresponding rational homology sphere YG.
|Original language||English (US)|
|Journal||Journal of Knot Theory and its Ramifications|
|State||Published - Jan 1 2016|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- knot Floer homology
- lattice homology