Quilted strips, graph associahedra, and A∞ n–modules

Ma’u, Sikimeti

doi:10.2140/agt.2015.15.783

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

Sikimeti Ma’u

Algebraic & Geometric Topology 15 (2015) 783–799

DOI: 10.2140/agt.2015.15.783

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

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

Volume 15, issue 2 (2015)