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We consider moduli spaces of quilted strips with markings and theircompactifications. Using the theory of moment maps of toric varieties weidentify the compactified moduli spaces with certain graph associahedra. Wedemonstrate how these moduli spaces govern the combinatorics of A-infinityn-modules, which are natural generalizations of A-infinity modules (n=1) andbimodules (n=2).

Quilted strips, graph associahedra, and A-infinity n-modules