# A framework for geometric field theories and their classification in dimension one

@article{Ludewig2020AFF, title={A framework for geometric field theories and their classification in dimension one}, author={M. Ludewig and A. Stoffel}, journal={arXiv: Differential Geometry}, year={2020} }

In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with a particular kind of geometric structure. We take particular care to establish a notion of smooth variation of geometric structures, so that it makes sense to require the output of our field theory functors to depend smoothly on the input. We then test our framework on the case of $1$-dimensional field theories (with or without orientation) over a manifold… CONTINUE READING

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