Manuel B�renz
Dichromatic state sum models for four-manifolds from pivotal functors
B�renz, Manuel; Barrett, John W.
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.
Citation
Bärenz, M., & Barrett, J. W. (2018). Dichromatic state sum models for four-manifolds from pivotal functors. Communications in Mathematical Physics, 360(2), https://doi.org/10.1007/s00220-017-3012-9
Journal Article Type | Article |
---|---|
Acceptance Date | Aug 27, 2017 |
Online Publication Date | Nov 24, 2017 |
Publication Date | Jun 30, 2018 |
Deposit Date | Oct 12, 2017 |
Publicly Available Date | Nov 24, 2017 |
Journal | Communications in Mathematical Physics |
Print ISSN | 0010-3616 |
Electronic ISSN | 1432-0916 |
Publisher | Springer Verlag |
Peer Reviewed | Peer Reviewed |
Volume | 360 |
Issue | 2 |
DOI | https://doi.org/10.1007/s00220-017-3012-9 |
Public URL | https://nottingham-repository.worktribe.com/output/943812 |
Publisher URL | https://link.springer.com/article/10.1007%2Fs00220-017-3012-9 |
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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0
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