Quantum Algebras, coalgebras and Invariants of Knots, Links and 3-Manifolds

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RADFORD, 98-02178 Abstract The proposer will continue his long term investigation into invariants of knots, 1-1 tangles and 3-manifolds which arise from various algebraic structures. The focus of this phase of his work is the study of quantum coalgebras and the invariants they determine. They account for the invariants which arise from finite dimensional quantum algebras. Coquasitriangular Hopf algebras are examples of quantum coalgebras. Hopf algebras and quantum groups are algebraic objects whose study is important in contemporary physics and also which have application to geometric and topological problems. Knot theory has seen applications in the studying molecular structure.