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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 equations of A n–modules.

Keywords
graph associahedra, toric varieties, moment map, A-infinity
Mathematical Subject Classification 2010
Primary: 14H10
Secondary: 14M25
References
Publication
Received: 9 December 2013
Revised: 10 September 2014
Accepted: 8 January 2015
Published: 22 April 2015
Authors
Sikimeti Ma’u
Department of Computer Science
Università degli Studi di Verona
Strada le Grazie 15
37134 Verona Italy