4 papers
The Kauffman bracket skein as an algebra of observables
D. Bullock, C. Frohman, J. Kania-Bartoszynska
We prove that the Kauffman bracket skein algebra of a cylinder over a surface with boundary, defined over complex numbers, is isomorphic to the observables of an appropriate lattic…
A matrix model for quantum SL_2
C. Frohman, J. Kania-Bartoszynska
We describe a topological ribbon Hopf algebra whose elements are sequences of matrices. The algebra is a quantum version of U(sl_2).
The Yang-Mills Measure in the Kauffman Bracket Skein Module
Doug Bullock, Charles Frohman, Joanna Kania-Bartoszynska
For each closed, orientable surface F, we construct a local, diffeomorphism invariant trace on the Kauffman bracket skein module K_t(F x [0,1]). The trace is defined when |t| is ne…
Quantum Obstruction Theory
Charles Frohman, Joanna Kania-Bartoszynska
We use topological quantum field theory to derive an invariant of a three-manifold with boundary. We then show how to use this invariant as an obstruction to embedding one three-ma…