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On Witten’s 3-manifold Invariants

- K. Walker
- Mathematics
- 2003

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… Expand

An Extension of Casson's Invariant.

- K. Walker
- Mathematics
- 3 March 1992

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… Expand

Fixing the functoriality of Khovanov homology

- D. Clark, Scott Morrison, K. Walker
- Mathematics
- 12 January 2007

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… Expand

(3+1)-TQFTs and topological insulators

- K. Walker, Zhenghan Wang
- Physics, Mathematics
- 13 April 2011

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… Expand

Man and machine thinking about the smooth 4-dimensional Poincaré conjecture

- M. Freedman, Robert E. Gompf, Scott Morrison, K. Walker
- Mathematics
- 28 June 2009

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… Expand

A class of P,T-invariant topological phases of interacting electrons

- M. Freedman, C. Nayak, K. Shtengel, K. Walker, Zhenghan Wang
- Physics
- 21 July 2003

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… Expand

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.… Expand

Positivity of the universal pairing in 3 dimensions

- Danny Calegari, M. Freedman, K. Walker
- Mathematics, Physics
- 21 February 2008

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… Expand

Universal manifold pairings and positivity

- M. Freedman, A. Kitaev, C. Nayak, J. Slingerland, K. Walker, Zhenghan Wang
- Mathematics
- 3 March 2005

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… Expand

Towards universal topological quantum computation in the ν = 5 2 fractional quantum Hall state

- M. Freedman, C. Nayak, K. Walker
- Physics
- 5 December 2005

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… Expand

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