### Abstract

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) |
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Article number | 1650003 |

Journal | Journal of Knot Theory and its Ramifications |

Volume | 25 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2016 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Keywords

- Knot
- L-space
- knot Floer homology
- lattice homology

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## Cite this

Ozsváth, P., Stipsicz, A. I., & Szabó, Z. (2016). Knot lattice homology in L-spaces.

*Journal of Knot Theory and its Ramifications*,*25*(1), [1650003]. https://doi.org/10.1142/S0218216516500036