Algebraic & Geometric Topology

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

Sikimeti Ma’u

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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 equations of A n–modules.

Article information

Algebr. Geom. Topol., Volume 15, Number 2 (2015), 783-799.

Received: 9 December 2013
Revised: 10 September 2014
Accepted: 8 January 2015
First available in Project Euclid: 28 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic)
Secondary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]

graph associahedra toric varieties moment map A-infinity


Ma’u, Sikimeti. Quilted strips, graph associahedra, and $A_\infty$ $n$–modules. Algebr. Geom. Topol. 15 (2015), no. 2, 783--799. doi:10.2140/agt.2015.15.783.

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