From polytopes to operads and back
K-Theory and Homology
2021-12-30 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.2112.13743,
title = {From polytopes to operads and back},
author = {Sergey Arkhipov and Daria Poliakova},
journal= {arXiv preprint arXiv:2112.13743},
year = {2021}
}
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28 pages