English

The Knot Floer Cube of Resolutions and the Composition Product

Geometric Topology 2017-03-03 v2

Abstract

We examine the relationship between the (untwisted) knot Floer cube of resolutions and HOMFLY-PT homology. By using a filtration induced by additional basepoints on the Heegaard diagram for a knot KK, we see that the filtered complex decomposes as a direct sum of HOMFLY-PT homologies of various subdiagrams. Jaeger's composition product formula shows that the graded Euler characteristic of this direct sum is the HOMFLY-PT polynomial of KK.

Keywords

Cite

@article{arxiv.1508.03037,
  title  = {The Knot Floer Cube of Resolutions and the Composition Product},
  author = {Nathan Dowlin},
  journal= {arXiv preprint arXiv:1508.03037},
  year   = {2017}
}

Comments

Last section moved to a later paper. Minor changes in notation