Floer homology and embedded bipartite graphs

Abstract

We generalize the construction of the Heegaard Floer homology for a singular knot to that for a balanced bipartite graph. For a given graph, we provide a combinatorial description of the Euler characteristic of its Heegaard Floer homology by using the "Kauffman states" on a graph diagram.

The paper is rewritten. We study balanced bipartite graphs, which generalize both trivalent graphs and singular knots. We show how to apply Alishahi and Eftekhary's refinement of sutured Floer homology to extract interesting invariants for a graph. In the latter half, we study the Alexander invariant of a graph, and calculate it for Kinoshita theta-graph as an example

References in corpus (1)

• Floer homology and knot complements

Cited by in corpus (5)

• A Cohomology Theory for Planar Trivalent Graphs with Perfect Matchings
• An Alexander polynomial for MOY graphs
• A topological interpretation of Viro's $\mathfrak{gl}(1|1)$-Alexander polynomial of a graph
• Alexander polynomial and spanning trees
• Grid homology for spatial graphs and a skein exact sequence