Double-point enhanced GRID invariants and Lagrangian cobordisms

2025/05/12 by Lewis, Ashton, Ojakli, Zachary, Petkova, Ina +1
#57K18 #57K33 (primary) #57R90 (secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2505.07599

Abstract

We define an invariant of Legendrian links in the double-point enhanced grid homology of a link, and prove that it obstructs decomposable Lagrangian cobordisms in the symplectization of the standard contact structure on \mathbb R³.

Citations

• Spectral GRID invariants and Lagrangian cobordisms
• Lagrangian cobordisms and Legendrian invariants in knot Floer homology
• Lagrangian concordance is not a symmetric relation
• Legendrian knots and exact Lagrangian cobordisms
• A combinatorial description of knot Floer homology
• Knot polynomials and knot homologies
• Holomorphic disks and knot invariants

Related

• Spectral GRID invariants and Lagrangian cobordisms
• Lagrangian cobordisms and Legendrian invariants in knot Floer homology
• Legendrian knots and exact Lagrangian cobordisms
• An obstruction to decomposable exact Lagrangian fillings
• Constructions of Lagrangian cobordisms