A Framework for Geometric Field Theories and their Classification in Dimension One

@article{Ludewig2021AFF,
  title={A Framework for Geometric Field Theories and their Classification in Dimension One},
  author={Matthias Ludewig and Augusto Stoffel},
  journal={Symmetry, Integrability and Geometry: Methods and Applications},
  year={2021}
}
In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such geometric structures, so that it makes sense to require the output of our field theory 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 M. Here the expectation… 
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