Rational tangles and the colored HOMFLY polynomial

The HOMFLY polynomial is an invariant of knots in S^3 which can be

extended to an invariant of tangles in B^3. I'll give a geometrical

description of this invariant for rational tangles, and

explain how this description extends to a more general invariant

(the lambda^k colored HOMFLY polynomial of a rational tangle). I'll then

use this description to sketch a proof of a conjecture of Gukov and Stosic

about the colored HOMFLY homology of rational knots.

Parts of this are joint work with Paul Wedrich and Mihaljo Cevic.