Deformations of lattice cohomology and the upsilon invariant

2020/10/15 by Antonio Alfieri, Alfieri, Antonio
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2010.07511

openalex publication_date 2020/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce deformations of lattice cohomology corresponding to the knot homologies found by Ozsv' ath, Stipsicz and Szab' o in \citeOSS4. 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.

Citations

• Floer homology and knot complements
• Holomorphic disks and knot invariants
• Holomorphic disks and topological invariants for closed three-manifolds
• Concordance homomorphisms from knot Floer homology

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