Math Stuff -- Kevin Walker

I can be reached at

I work at Microsoft Station Q.

New TQFT notes: TQFTs [version 1h, 11 May 2006]. This is an early, incomplete draft. There are notational (and other) inconsistencies, and some parts have not been proof-read. Still, it's probably better than nothing. I plan on updating it frequently.

1991 TQFT notes: "On Witten's 3-manifold Invariants".

Other papers etc.:

• Higher categories, colimits, and the blob complex (with Scott Morrison); a more concise, less detailed version of the longer blob paper; to appear in Proceedings of the National Academy of Sciences, draft version available here
• The Blob Complex (with Scott Morrison) math.AT/1009.5025, but this version (13 Dec 2011) might be more up to date
• Projective Ribbon Permutation Statistics: a Remnant of non-Abelian Braiding in Higher Dimensions (with Michael Freedman, Matthew B. Hastings, Chetan Nayak, Xiao-Liang Qi, Zhenghan Wang) physics.mes-hall/1005.0583 or Phys. Rev. B 83, 115132 (2011)
• Man and machine thinking about the smooth 4-dimensional Poincaré conjecture (with Michael Freedman, Robert Gompf and Scott Morrison) math.GT/0906.5177 or Quantum Topology Vol. 1 Issue 2 (2010) 171-208
• An orthogonal approach to the subfactor of a planar algebra (with Vaughan Jones and Dimitri Shlyakhtenko), math.OA/0807.4146 or Pacific Journal of Mathematics Vol. 246 (2010), No. 1, 187-197
• On Picture (2+1)-TQFTs (with Michael Freedman, Chetan Nayak and Zhenghan Wang), math.QA/0806.1926 or Proceedings of the Nankai International Conference in Memory of Xiao-Song Lin (Nankai Tracts in Mathematics, Vol. 12)
• Positivity of the universal pairing in 3 dimensions (with Danny Calegari and Michael Freedman), math.GT/0802.3208 or Jour. Amer. Math. Soc. 23 (2010), no. 1, 107-188
• Fixing the functoriality of Khovanov homology (with David Clark and Scott Morrison), math.GT/0701339 or Geometry & Topology 13 (2009) 1499-1582
• Noncommuting Flux Sectors in a Tabletop Experiment (with Alexei Kitaev and Gregory W. Moore), hep-th/0706.3410
• From String Nets to Nonabelions (with Lukasz Fidkowski, Michael Freedman, Chetan Nayak and Zhenghan Wang), cond-mat/0610583 or Commun. Math. Phys. 287, 805-827 (2009)
• Tilted Interferometry Realizes Universal Quantum Computation in the Ising TQFT without Overpasses (with Michael Freedman and Chetan Nayak), cond-mat/0512072
• Towards Universal Topological Quantum Computation in the ν=5/2 Fractional Quantum Hall State (with Michael Freedman and Chetan Nayak), cond-mat/0512066 or Phys. Rev. B 73, 245307 (2006)
• Universal Manifold Pairings and Positivity (with Michael Freedman, Alexei Kitaev, Chetan Nayak, Johannes K. Slingerland and Zhenghan Wang), math.GT/0503054 or Geometry and Topology 9 (2005) 2303-2317
• A Class of P,T-Invariant Topological Phases of Interacting Electrons (with Michael Freedman, Chetan Nayak, Kirill Shtengel and Zhenghan Wang), cond-mat/0307511 or Annals of Physics 310 (2004) 428-492
• Quantum SU(2) faithfully detects mapping class groups modulo center (with Michael Freedman and Zhenghan Wang), math.GT/0209150 or Geometry and Topology 6 (2002) 523-539
• An Extension of Casson's Invariant, Princeton University Press, 1992, ISBN 0-691-02532-0, Amazon or P.U.P. (One of these days I'll make a PDF version available here. In the meantime, someone donated this DjVu version.)
• An extension of Casson's invariant to rational homology spheres, Bull. Amer. Math. Soc. 22 (1990), 261-267
• Configuration Spaces of Linkages, undergraduate thesis, Princeton University, 1985, scanned PDF version

I don't necessarily recommend it, but you can also try to decipher my slides from talks.