Quantum supergroups and topological invariants of three - manifolds


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, Uq(gl(2∣1))U_q(gl(2|1)) at odd roots of unity is studied in detail, and the corresponding topological invariants are obtained.Comment: 22 page

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