Floer homology and embedded bipartite graphs
Geometric Topology
2018-09-24 v4
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.
Keywords
Cite
@article{arxiv.1401.6608,
title = {Floer homology and embedded bipartite graphs},
author = {Yuanyuan Bao},
journal= {arXiv preprint arXiv:1401.6608},
year = {2018}
}
Comments
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