English

The skein polynomial of closed 3-braids

Geometric Topology 2008-08-30 v2

Abstract

Using the band representation of the 3-strand braid group, it is shown that the genus of 3-braid links can be read off their skein polynomial. Some applications are given, in particular a simple proof of Morton's conjectured inequality and a condition to decide that some polynomials, like the one of 9_{49}, are not admitted by 3-braid links. Finally, alternating links of braid index 3 are classified.

Keywords

Cite

@article{arxiv.math/0103041,
  title  = {The skein polynomial of closed 3-braids},
  author = {A. Stoimenow},
  journal= {arXiv preprint arXiv:math/0103041},
  year   = {2008}
}

Comments

10 pages; revision 1 Apr 01: minor changes, added remarks on question 4