nLab
Yetter model

Context

\infty-Chern-Simons theory

Ingredients

Definition

Examples

  • For targets

  • For targets

  • For discrete targets

  • For targets

    • coupled to
  • For targets extending the

    (such as the , the )

    • Chern-Simons-

  • for higher abelian targets

  • for targets

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  • for the L L_\infty-structure on the of the closed :

Quantum field theory

Contents

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  • FQFT and

Physics

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Surveys, textbooks and lecture notes

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    • Axiomatizations

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    • Tools

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    • Structural phenomena

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Contents

Idea

The Yetter model is a 4d TQFT sigma-model quantum field theory whose target space is a discrete 2-groupoid and whose background gauge field is a circle 4-bundle.

Together with the Dijkgraaf-Witten model these form the first two steps in filtering of target spaces by homotopy type truncation of ∞-Chern-Simons theory with discrete target spaces. It is hence also an example of a 4d Chern-Simons theory.

The Yetter model is not the same as the Crane-Yetter model.

Definition

Fix

The Yetter-model is the ∞-Dijkgraaf-Witten theory induced by this data.

References

The model without a background gauge field/cocycle was considered in

  • David Yetter, TQFTs from homotopy 2-types , Journal of Knot Theory and its Ramifications 2 (1993), 113-123.

The effect of having a nontrivial group 4-cocycle was considered (but now only on a 1-group) in

  • D. Birmingham, M. Rakowski, On Dijkgraaf-Witten Type Invariants, Lett. Math. Phys. 37 (1996), 363.

  • Marco Mackaay, Spherical 2-categories and 4-manifold invariants, Adv. Math. 153 (2000), no. 2, 353–390. (arXiv:math/9805030)

    .

The reinterpretation of the “state sum” equation used in the above publications as giving homomorphisms of simplicial sets/topological spaces is given in

  • Tim Porter, Interpretations of Yetter’s notion of GG-coloring : simplicial fibre bundles and non-abelian cohomology, Journal of Knot Theory and its Ramifications 5 (1996) 687-720,

and then extended to colorings in homotopy n-types in

  • Tim Porter, Topological Quantum Field Theories from Homotopy n-types, Journal of the London Math. Soc. (2) 58 (1998) 723-732.

See also

  • João Faria Martins and Tim Porter, On Yetter’s invariants and an extension of the Dijkgraaf-Witten invariant to categorical groups, Theory and Applications of Categories, Vol. 18, 2007, No. 4, pp 118-150.

    (TAC)

which has some remarks about higher (2-)group cocycles towards the end.

Last revised on November 18, 2014 at 22:13:22. See the history of this page for a list of all contributions to it.