Invariants of 3-Manifolds Associated with Quantum Groups and Verlinde's Formula

Abstract

We obtain a projectively linear representation of $SL(2,\mathbf{Z})$ from invariants defined by Reshetikhin and Turaev and prove ‘Verlinde's formula’ for $SU(2)$ based on the computation of invariants. Using an algebra associated with ‘Ising model’, we constract invariants of links and 3-manifolds.