English

Invariants of closed braids via counting surfaces

Geometric Topology 2015-03-20 v3

Abstract

A Gauss diagram is a simple, combinatorial way to present a link. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting subdiagrams of certain combinatorial types. In this paper we present simple formulas for an infinite family of invariants in terms of counting surfaces of a certain genus and number of boundary components in a Gauss diagram associated with a closed braid. We then identify the resulting invariants with partial derivatives of the HOMFLY-PT polynomial.

Keywords

Cite

@article{arxiv.1209.1308,
  title  = {Invariants of closed braids via counting surfaces},
  author = {Michael Brandenbursky},
  journal= {arXiv preprint arXiv:1209.1308},
  year   = {2015}
}

Comments

This is a revised version. To appear in JKTR. arXiv admin note: text overlap with arXiv:1209.0420