Geometric realizations of the multiplihedra

By S. Ma’u, Christopher Woodward. Compositio Mathematica, 2010

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A generalization of manifolds with corners (2015, background): “Ma’u and Woodward [22] define moduli spaces Mn,1 of ‘stable n-marked quilted discs’.”
Generating the Fukaya categories of Hamiltonian 𝐺-manifolds (2015, background): “The A∞ -equations follow from the fact that these compactifications are homeomorphic to associahedra [42, 43, 44].”
On partially wrapped Fukaya categories (2016, background): “nity, modulo translation. This space, suitably compactied, realizes Stashe’s multiplihedra. For other, nicer descriptions of the multiplihedra in the context of Floer theory, we refer the reader to [29]. To achieve associativity of strip-like end gluing in the boundary charts, we rst need an auxilia”
QUANTUM KIRWAN MORPHISM AND GROMOV-WITTEN INVARIANTS OF QUOTIENTS I (2012, background): “(d) (Cutting edges with relations) Υ : Γ → Γ′ cuts edges with relations of Γ if the vertices are the same, but Γ′ has fewer edges than Γ, with each removed edge lying on a path between the root edge and the colored vertices, and each path passing through a unique such edge.”