Some computations on instanton knot homology.

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 3 -manifolds. In this paper, for a knot inside S 3 , we further introduce an algorithm that computes an upper bound of the dimension of instanton knot homology from knot diagrams. We test the algorithm with all knots up to seven crossings as well as a more complicated knot 1 0 1 5 3 . 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 be an instanton L-space knot. [ABSTRACT FROM AUTHOR]