The skein polynomial of closed 3-braids

Details The skein polynomial of closed 3-braids The skein polynomial of closed 3-braids

2001-03-06

arxiv.org/abs/math/0103041v2

J. Reine Angew. Math. 564 (2003), 167--180.

Mathematics

Geometric Topology

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

Scientific paper

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.

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