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K-State Today

April 6, 2017

Mathematics Colloquium Lecture April 6

By Reta McDermott

Thomas Kerler, Ohio State University, will present "Hopf Algebra Bundles and Links on Surfaces" as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Thursday, April 6, in 122 Cardwell Hall.

The abstract for the lecture is: (Based on joint work with and dissertation of Alex Borland). Hopf algebras with additional structures have been successfully used to combinatorially construct strong invariants of knots, links, and tangles — represented by diagrams in the plane — using only Hopf algebra operations. They dominate many of the modern knot polynomials. We explain and extend the Hopf algebraic construction to link diagrams on surfaces which use fibers of a flat ribbon Hopf algebra bundle over the surface for local assignments rather than a single fixed Hopf algebra. Our construction is motivated by and encompasses Turaev's version of the Jones polynomial with an additional parameter that provides an invariant for his knotoids.

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