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Closed subsets of the Weyl alcove and TQFTs
Stephen F. Sawin
For an arbitrary simple Lie algebra $\g$ and an arbitrary root of unity the closed subsets of the Weyl alcove of the quantum group $U_q(\g)$ are classified. Here a closed subs…
Three-Dimensional 2-Framed TQFTs and Surgery
Stephen Sawin
The notion of 2-framed three-manifolds is defined. The category of 2-framed cobordisms is described, and used to define a 2-framed three-dimensional TQFT. Using skeletonization and…
Invariants of Spin Three-Manifolds From Chern-Simons Theory and Finite-Dimensional Hopf Algebras
Stephen F. Sawin
A version of Kirby calculus for spin and framed three-manifolds is given and is used to construct invariants of spin and framed three-manifolds in two situations. The first is ribb…
Jones-Witten Invariants for Nonsimply-Connected Lie Groups and The Geometry of the Weyl Alcove
Stephen F. Sawin
The quotient process of Müger and Bruguières is used to construct modular categories and TQFTs out of closed subsets of the Weyl alcove of a simple Lie algebra. In particular it is…