  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.
