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arXiv · 1312.7561

Two-dimensional state sum models and spin structures

John W. Barrett·Sara O. G. Tavares
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Abstract

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 augmented with a crossing map, the partition function is defined for any oriented surface with a spin structure. An algebraic condition that is necessary for the state sum model to be sensitive to spin structure is determined. Some examples of state sum models that distinguish topologically-inequivalent spin structures are calculated.

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BibTeXRIS

John W. Barrett, Sara O. G. Tavares. 2015-03-13. Two-dimensional state sum models and spin structures. https://doi.org/10.1007/s00220-014-2246-z

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