TL;DR
This paper establishes a surgery exact triangle for lattice cohomology, an invariant of 3-manifolds, aligning it more closely with Heegaard Floer homology and aiding in their comparison.
Contribution
It proves a surgery exact triangle for lattice cohomology, a key step in relating it to Heegaard Floer homology.
Findings
Proved a surgery exact triangle for lattice cohomology.
Enhanced understanding of the relationship between lattice cohomology and HF^+.
Facilitated future comparisons of these invariants.
Abstract
Lattice cohomology, defined by N\'emethi in (arXiv:0709.0841), is an invariant of negative definite plumbed 3-manifolds which conjecturally computes the Heegaard Floer homology HF^+. We prove a surgery exact triangle for the lattice cohomology analogous to the one for HF^+. This is a step towards comparing these two invariants.
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