3-Manifold Seminar: Reshetikhin-Turaev TQFTs and a Spin TQFT related to the Ising Category

Seminar | April 30 | 3:40-5 p.m. | 736 Evans Hall

 Kevin Donoghue, UC Berkeley

 Department of Mathematics

Around 1990, Reshetikhin and Turaev discovered a family of 3d TQFTs whose relation to the rest of 3-manifold topology is still poorly understood. The biggest obstruction to relating these TQFTs to the rest of the 3-manifold world is that their original construction is almost entirely algebraic. For closed manifolds, Kirby and Melvin managed to relate one of these TQFTs to some classical invariants of Spin manifolds. For 3-manifolds with boundary (or, especially, surfaces with boundary), the relation of this TQFT to classical topology is trickier and not so geometrically motivated. This talk will motivate and sketch a purely topological construction of a very closely related Spin TQFT. Rather than produce a family of topological invariants from algebra, this construction produces algebra from a family of topological invariants. The general Reshetikhin-Turaev construction of TQFTs will be reviewed.