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.
%0 Generic
%1 Barrett2014Twodimensional
%A Barrett, John W.
%A Tavares, Sara O. G.
%D 2014
%K spin
%T Two-dimensional state sum models and spin structures
%U http://arxiv.org/abs/1312.7561
%X 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.
@misc{Barrett2014Twodimensional,
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.}},
added-at = {2019-02-23T22:09:48.000+0100},
archiveprefix = {arXiv},
author = {Barrett, John W. and Tavares, Sara O. G.},
biburl = {https://www.bibsonomy.org/bibtex/230386ba7f38f4e9a457a1b4c42d49b55/cmcneile},
citeulike-article-id = {13364839},
citeulike-linkout-0 = {http://arxiv.org/abs/1312.7561},
citeulike-linkout-1 = {http://arxiv.org/pdf/1312.7561},
day = 20,
eprint = {1312.7561},
interhash = {4c521147b3797f8c5c7a19221ee91d0e},
intrahash = {30386ba7f38f4e9a457a1b4c42d49b55},
keywords = {spin},
month = feb,
posted-at = {2014-09-16 14:59:37},
priority = {2},
timestamp = {2019-02-23T22:15:27.000+0100},
title = {{Two-dimensional state sum models and spin structures}},
url = {http://arxiv.org/abs/1312.7561},
year = 2014
}