Pure Maths Colloquium: The meridian maps in skein theory
7 February 2005 16:00 in CM221
"The meridian map is an endomorphism of the linear skein of the annulus, induced by placing an extra meridian loop around any diagram in the annulus. The eigenvalues of this map depend on two partitions, and all occur with multiplicity 1. The corresponding eigenvectors form a natural basis in many constructions of knot and manifold invariants, and they play a key role in the transition between the quantum $SL(N,q)$ invariants of a knot and its Homfly invariants. I shall introduce skein theory in this context and give an account of some of the simple skein theoretic features used in constructing the eigenvectors, and their resulting properties. "
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