Some Computations on Instanton Knot Homology
Abstract
In a recent paper, the first author and his collaborator developed a method to compute an upper bound of the dimension of instanton Floer homology via Heegaard Diagrams of 3manifolds. For a knot inside S3, we further develop an algorithm that can compute an upper bound of the dimension of instanton knot homology from knot diagrams. We test the effectiveness of the algorithm and found that for all knots up to seven crossings, the algorithm provides sharp bounds. In the second half of the paper, we show that, if the instanton knot Floer homology of a knot has a specified form, then the knot must an instanton Lspace knot.
 Publication:

arXiv eprints
 Pub Date:
 February 2021
 DOI:
 10.48550/arXiv.2102.07300
 arXiv:
 arXiv:2102.07300
 Bibcode:
 2021arXiv210207300L
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Algebraic Topology
 EPrint:
 accepted version