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arXiv · 2112.13743

From polytopes to operads and back

Sergey Arkhipov·Daria Poliakova
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Abstract

For a directed polytope, we construct a colored operad whose Poincare-Hilbert series encodes certain operations on the cellular complex of the polytope. We conjecture that for a class of short polytopes the constructed operads are Koszul and self-dual. We verify the conjecture for simplices, polygons, and products thereof.

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Sergey Arkhipov, Daria Poliakova. 2021-12-27. From polytopes to operads and back. https://arxiv.org/abs/2112.13743

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