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The meridian maps in skein theory
by
Hugh R. Morton
University of Liverpool, UK
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 for the Homfly skein 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 give an account of some of the simple skein theoretic features used in constructing the eigenvectors, and their resulting properties.
Date received: January 17, 2005
Copyright © 2005 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # capo-04.