Dichromatic state sum models for four-manifolds from pivotal functors

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Bärenz, Manuel and Barrett, John W. (2018) Dichromatic state sum models for four-manifolds from pivotal functors. Communications in Mathematical Physics, 360 (2). pp. 663-714. ISSN 1432-0916

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Official URL: https://link.springer.com/article/10.1007%2Fs00220-017-3012-9

Abstract

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.

Item Type:	Article
RIS ID:	https://nottingham-repository.worktribe.com/output/943812
Schools/Departments:	University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number:	https://doi.org/10.1007/s00220-017-3012-9
Depositing User:	Eprints, Support
Date Deposited:	12 Oct 2017 07:46
Last Modified:	04 May 2020 19:43
URI:	https://eprints.nottingham.ac.uk/id/eprint/47124

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