Quantum supergroups and topological invariants of three-manifolds

Abstract

The Reshetikhin-Turaev approach to topological invariants of three-manifolds is generalized to quantum supergroups. A general method for constructing three-manifold invariant 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)) at odd roots of unity is studied in detail, and the corresponding topological invariants are obtained.