The skein polynomial of closed 3-braids
arXiv:math/0103041
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.
10 pages; revision 1 Apr 01: minor changes, added remarks on question 4