The affine associahedron sphere conjecture
An affine associahedron is the dual of the quotient cluster complex associated with an affine cluster algebra, and its dimension is determined by the rank of that algebra. The affine associahedron sphere conjecture. Each affine associahedron is topologically a sphere. The paper provides inductive counting formulas for its facets, while the claimed global topology remains conjectural.
References
Primary source
Dani Kaufman and Zachary Greenberg, “Cluster Modular Groups of Affine and Doubly Extended Cluster Algebras”, arXiv:2107.10334 (2025).
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