### Abstract

Assume that F_{v0} is a tree with vertex set Vert (F_{υ0}) = {v_{0}, v_{1}, ... , v_{n}}, and with an integral framing (weight) attached to each vertex except v_{0}. Assume furthermore that the intersection matrix of G = F_{v0} - {v_{0}} is negative definite. We define a filtration on the chain complex computing the lattice homology of G and show how to use this information in computing lattice homology groups of a negative definite graph we get by attaching some framing to υ_{0}. As a simple application we produce new families of graphs which have arbitrarily many bad vertices for which the lattice homology groups are isomorphic to the corresponding Heegaard Floer homology groups.

Original language | English (US) |
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Pages (from-to) | 783-818 |

Number of pages | 36 |

Journal | Commentarii Mathematici Helvetici |

Volume | 89 |

Issue number | 4 |

DOIs | |

State | Published - 2014 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Keywords

- Heegaard Floer homology
- Knot Floer homology
- Lattice homology

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## Cite this

*Commentarii Mathematici Helvetici*,

*89*(4), 783-818. https://doi.org/10.4171/CMH/334