|
Organizers |
Vassiliev Theory as Deformation Theory
by
David N. Yetter
Dept. of Mathematics, Kansas State University
It would appear to be fruitful to consider Vassiliev invariants of knots, links, and tangles in the context of an algebraic deformation theory for braided monoidal categories.
We describe the construction of cochain complexes associated to monoidal categories, monoidal functors, and braided monoidal categories, and theorems relating the cohomology of the category (functor) to infinitesimal deformations of its structure maps.
When a symmetric monoidal category with duals is deformed to give rise to a ribbon category, the kth term in the functorial link invariant associated to the deformed category is seen to be a Vassiliev invariant of degree≤ k.
Ëxtrinsic deformations" in which a braided monoidal category is deformed a subcategory of a larger category are shown to provide a setting for the consideration of universal Vassiliev invariants over general coefficient rings.
Date received: February 28, 2000
Copyright © 2000 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 # caea-30.