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On Witten’s 3-manifold Invariants
I distributed a preliminary version of some notes on Witten's recently discovered 3-manifold invariants. For various reasons the paper was never completed and published. Nevertheless, many people
An Extension of Casson's Invariant.
This monograph describes an invariant, lambda, of oriented rational homology 3-spheres, which is a generalization of Andrew Casson's work in the integer homology sphere case. A formula describing how
Fixing the functoriality of Khovanov homology
We describe a modification of Khovanov homology [13], in the spirit of Bar-Natan [2], which makes the theory properly functorial with respect to link cobordisms. This requires introducing
(3+1)-TQFTs and topological insulators
Levin-Wen models are microscopic spin models for topological phases of matter in (2+1)-dimension. We introduce a generalization of such models to (3 + 1)-dimension based on unitary braided fusion
Man and machine thinking about the smooth 4-dimensional Poincaré conjecture
While topologists have had possession of possible counterexamples to the smooth 4-dimensional Poincare conjecture (SPC4) for over 30 years, until recently no invariant has existed which could
A class of P,T-invariant topological phases of interacting electrons
Abstract We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by
Fermion condensation and super pivotal categories
We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain a fermion.
Positivity of the universal pairing in 3 dimensions
Associated to a closed, oriented surface S is the complex vector space with basis the set of all compact, oriented 3-manifolds which it bounds. Gluing along S defines a Hermitian pairing on this
Universal manifold pairings and positivity
Gluing two manifolds M1 and M2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x = �aiMi yields a sesquilinear pairing p = h , i with values in (formal
Towards universal topological quantum computation in the ν = 5 2 fractional quantum Hall state
The Pfaffian state, which may describe the quantized Hall plateau observed at Landau level filling fraction $\ensuremath{\nu}=\frac{5}{2}$, can support topologically-protected qubits with extremely