A surgery triangle for lattice cohomology

Abstract

Lattice cohomology, defined by Némethi in [Publ. Res. Inst. Math. Sci. 44 (2008) 507–543], is an invariant of negative definite plumbed $3$–manifolds which conjecturally computes their Heegaard Floer homology $H{F}^{+}$. We prove a surgery exact triangle for the lattice cohomology analogous to the one for $H{F}^{+}$. This is a step towards relating these two invariants.