Research Repository

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Dichromatic state sum models for four-manifolds from pivotal functors (2017)
Journal Article
Bärenz, M., & Barrett, J. W. (2018). Dichromatic state sum models for four-manifolds from pivotal functors. Communications in Mathematical Physics, 360(2), doi:10.1007/s00220-017-3012-9. ISSN 0010-3616

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 ri... Read More

Monte Carlo simulations of random non-commutative geometries (2016)
Journal Article
Barrett, J. W., & Glaser, L. (2016). Monte Carlo simulations of random non-commutative geometries. Journal of Physics A: Mathematical and Theoretical, 49(24), doi:10.1088/1751-8113/49/24/245001. ISSN 1751-8113

Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest types of Clifford algebra are investigated using Monte C... Read More

Two-dimensional state sum models and spin structures (2014)
Journal Article
Barrett, J. W., & Tavares, S. O. G. (2014). Two-dimensional state sum models and spin structures. Communications in Mathematical Physics, 336(1), 63-100. doi:10.1007/s00220-014-2246-z

The state sum models in two dimensions introduced by Fukuma, Hosono and Kawai are generalised by allowing algebraic data from a non-symmetric Frobenius algebra. Without any further data, this leads to a state sum model on the sphere. When the data is... Read More