Quantum supergroups and topological invariants of three - manifolds

Abstract

The Reshetikhin - Turaeve approach to topological invariants of three - manifolds is generalized to quantum supergroups. A general method for constructing three - manifold invariants is developed, which requires only the study of the eigenvalues of certain central elements of the quantum supergroup in irreducible representations. To illustrate how the method works, $U_q(gl(2|1))$ at odd roots of unity is studied in detail, and the corresponding topological invariants are obtained.

22 pages

References in corpus (1)

• A Large k Asymptotics of Witten's Invariant of Seifert Manifolds

Cited by in corpus (10)

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• Infinitely many two-variable generalisations of the Alexander-Conway polynomial
• Geometry and Representations of the Quantum Supergroup OSPq(1|2n)
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• On the Harish-Chandra Homomorphism for Quantum Superalgebras
• Solutions to the Yang-Baxter Equation and Casimir Invariants for the Quantised Orthosymplectic Superalgebra
• The Birman-Wenzl-Murakami algebra, Hecke algebra and representations of U_{q}(osp(1|2n))
• Integrable representations of the quantum affine special linear superalgebra
• The Links-Gould Invariant of Links
• Structure And Representations Of The Quantum General Linear Supergroup