arXiv:math/0009118math.HO
Finding topology in a factory: configuration spaces
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Abstract
This expository article describes applications of topological configuration spaces to the control of robotic systems. In particular, we review recent work by the authors on configuration spaces of graphs. These are lovely spaces: we show for example that the configuration space of two points on the complete graph of five vertices is a closed orientable surface of genus six.
This is a decent place to get started https://arxiv.org/pdf/math/0009118.pdf You can extend some of the thinking in this paper to cover action spaces for deep RL models to really have some fun!
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