On grid homology for lens space links: combinatorial invariance and integral coefficients

2021/10/01 by Samuel Tripp, Tripp, Samuel
Mathematics · #57K10 (Secondary) #57K18 (Primary) #57R58 (Secondary) #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.2110.00663

openalex publication_date 2021/10/01 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

Abstract

Following the approach to grid homology of links in S³, we prove combinatorially that the grid homology of links in lens spaces defined by Baker, Grigsby, and Hedden is a link invariant. Further, using the sign assignment defined by Celoria, we prove that the generalization of grid homology to integral coefficients is a link invariant.

Citations

• Floer homology and knot complements
• Holomorphic disks and knot invariants
• Grid Diagrams and Legendrian Lens Space Links

Related

• Grid homology for singular links in lens space and a resolution cube
• Equivalence of two diagram representations of links in lens spaces and essential invariants
• Grid invariants in universally tight lens spaces
• A note on Grid Homology in lens spaces: ℤ coefficients and computations
• Grid Diagrams and Legendrian Lens Space Links