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

TL;DR

This paper explores the connection between moduli spaces of quilted strips, graph associahedra, and A-infinity n-modules, revealing new geometric and combinatorial insights into their structure and relationships.

Contribution

It introduces a novel identification of compactified moduli spaces with graph associahedra and links these to the combinatorics of A-infinity n-modules.

Findings

Moduli spaces of quilted strips are identified with graph associahedra.

The structure of A-infinity n-modules is governed by these moduli spaces.

The work generalizes known concepts from A-infinity modules and bimodules.

Abstract

We consider moduli spaces of quilted strips with markings and their compactifications. Using the theory of moment maps of toric varieties we identify the compactified moduli spaces with certain graph associahedra. We demonstrate how these moduli spaces govern the combinatorics of A-infinity n-modules, which are natural generalizations of A-infinity modules (n=1) and bimodules (n=2).