Deformations of lattice cohomology and the upsilon invariant

Abstract

We introduce deformations of lattice cohomology corresponding to the knot homologies found by Ozsv\' ath, Stipsicz and Szab\' o in \cite{OSS4}. By means of holomorphic triangles counting, we prove equivalence with the analytic theory for a wide class of knots. This yields combinatorial formulae for the upsilon invariant.

25 pages, 2 figures

References in corpus (2)

• Floer homology and knot complements
• Instanton Floer homology of almost-rational plumbings