2008/04/18 by Kenneth L. Baker, Baker, Kenneth L., J. Elisenda Grigsby +1 · 2 citations
Mathematics · Medicine · #53D10 #57M27 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.0804.3048
openalex publication_date 2008/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Grid diagrams encode useful geometric information about knots in S3. In particular, they can be used to combinatorially define the knot Floer homology of a knot K in S3, and they have a straightforward connection to Legendrian representatives of K in (S3, ξ_\st), where ξ_\st is the standard, tight contact structure. The definition of a grid diagram was extended to include a description for links in all lens spaces, resulting in a combinatorial description of the knot Floer homology of a knot K in L(p, q) for all p > 0. In the present article, we explore the connection between lens space grid diagrams and the contact topology of a lens space. Our hope is that an understanding of grid diagrams from this point of view will lead to new approaches to the Berge conjecture, which claims to classify all knots in S3 upon which surgery yields a lens space.