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arXiv:math/0103041 [math.GT]AbstractReferencesReviewsResources

The skein polynomial of closed 3-braids

A. Stoimenow

Published 2001-03-06, updated 2001-04-01Version 2

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.

Comments: 10 pages; revision 1 Apr 01: minor changes, added remarks on question 4
Journal: J. Reine Angew. Math. 564 (2003), 167--180.
Categories: math.GT
Subjects: 57M25
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