nLab Vladimir Turaev

Vladimir Turaev is a mathematician of Russian origin, who has made fundamental contributions to Quantum Field Theory, low dimensional topology, knot theory, and their interactions with mathematical physics and algebra.

He is currently based at Indiana University (Home page which is not very informative!)

Selected writings

• On certain enumeration problems in two-dimensional topology , Math. Res. Lett.16(3) (2009), 515-529.

Introducing the Reshetikhin-Turaev construction:

• Nikolai Reshetikhin, Vladimir Turaev, Invariants of 3-manifolds via link polynomials and quantum groups. Invent. Math. 103 (1991), no. 3, 547–597. (doi:10.1007/BF01239527, pdf)

On knot theory (knot invariants) and 3-manifolds:

• Vladimir Turaev: Quantum invariants of knots and 3-manifolds, de Gruyter Studies in Mathematics 18, de Gruyter & Co. (1994) [doi:10.1515/9783110435221, pdf]

On homotopy quantum field theory:

• Vladimir Turaev (with appendices by Michael Müger and Alexis Virelizier): Homotopy Quantum Field Theory, Tracts in Mathematics 10, European Mathematical Society (2010) [ems:etm/79]

On Dijkgraaf-Witten theory:

• Dijkgraaf-Witten invariants of surfaces and projective representations of groups, J. Geom. Phys. 57(11) (2007), 2419-2430.

On braid groups:

• Christian Kassel, Vladimir Turaev, Braid Groups, GTM 247 Springer Heidelberg 2008 (doi:10.1007/978-0-387-68548-9, webpage)

Related entries

• Reshetikhin-Turaev construction

• Reshetikhin-Turaev invariant

• Turaev-Viro model

• unitary functorial field theory

category: people