Dichromatic state sum models for four-manifolds from pivotal functors
A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category. A state sum formula for the...
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| Format: | Article |
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Springer
2018
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| Online Access: | https://eprints.nottingham.ac.uk/47124/ |
| Summary: | A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category.
A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary ribbon fusion category is recovered, including the nonmodular case. It is shown that the Crane-Yetter invariant for nonmodular categories is stronger than signature and Euler invariant.
A special case is the four-dimensional untwisted Dijkgraaf-Witten model. Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models.
Relations to different approaches to quantum gravity such as Cartan geometry and teleparallel gravity are also discussed. |
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