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