#### Volume 15, issue 2 (2015)

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Quilted strips, graph associahedra, and $A_\infty$ $n$–modules

### Sikimeti Ma’u

Algebraic & Geometric Topology 15 (2015) 783–799
##### Abstract

We consider moduli spaces of quilted strips with markings. By identifying each compactified moduli space with the nonnegative real part of a projective toric variety, we conclude that it is homeomorphic under the moment map to the moment polytope. The moment polytopes in these cases belong to a certain class of graph associahedra, which include the associahedra and permutahedra as special cases. In fact, these graph associahedra are precisely the polytopes whose facet combinatorics encode the ${A}_{\infty }$ equations of ${A}_{\infty }$ $n$–modules.

##### Keywords
graph associahedra, toric varieties, moment map, A-infinity
Primary: 14H10
Secondary: 14M25