The Fukaya category of the pillowcase, traceless character varieties, and Khovanov cohomology

DOI10.1090/tran/8116OpenAlexW2888716335MaRDI QIDQ5147426

Matthew Hedden, Christopher M. Herald, Paul A. Kirk, Matthew Hogancamp

Publication date: 26 January 2021

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.06957

Mathematics Subject Classification ID

Symplectic aspects of Floer homology and cohomology (53D40) Floer homology (57R58) Knot theory (57K10) Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.) (57K18)

Related Items

The correspondence induced on the pillowcase by the earring tangle, Holonomy perturbations of the Chern-Simons functional for lens spaces

Cites Work

• A type \(D\) structure in Khovanov homology
• The symplectic arc algebra is formal
• A self-pairing theorem for tangle Floer homology
• Khovanov homology is an unknot-detector
• Flat surfaces and stability structures
• A functor-valued invariant of tangles
• A type A structure in Khovanov homology
• A link invariant from the symplectic geometry of nilpotent slices
• Fukaya categories and Picard-Lefschetz theory
• The pillowcase and traceless representations of knot groups. II: A Lagrangian-Floer theory in the pillowcase
• Holonomy perturbations and regularity for traceless SU(2) character varieties of tangles
• A categorification of the Jones polynomial
• Bordered theory for pillowcase homology
• Khovanov's homology for tangles and cobordisms
• On bordered theories for Khovanov homology
• On the Fukaya categories of higher genus surfaces
• A cylindrical reformulation of Heegaard Floer homology
• The pillowcase and perturbations of traceless representations of knot groups
• A Beginner’s Introduction to Fukaya Categories
• On the traceless SU(2) character variety of the 6-punctured 2-sphere
• Fukaya categories and bordered Heegaard-Floer homology
• Knot homology groups from instantons
• Graded lagrangian submanifolds
• Bordered Heegaard Floer homology
• Homological Algebra of Mirror Symmetry
• Fukaya categories of the torus and Dehn surgery
• Khovanov homology from Floer cohomology
• Peculiar modules for 4‐ended tangles
• Fukaya categories of symmetric products and bordered Heegaard-Floer homology
• Homological mirror symmetry for punctured spheres