Algebraic & Geometric Topology 8 (2008) 2081–2108

DOI: 10.2140/agt.2008.8.2081

Abstract

Given a graph G, we construct a convex polytope whose face poset is based on marked subgraphs of G. Dubbed the graph multiplihedron, we provide a realization using integer coordinates. Not only does this yield a natural generalization of the multiplihedron, but features of this polytope appear in works related to quilted disks, bordered Riemann surfaces and operadic structures. Certain examples of graph multiplihedra are related to Minkowski sums of simplices and cubes and others to the permutohedron.

Keywords

multiplihedron, graph associahedron, realization, convex hull

Mathematical Subject Classification

Primary: 52B11

Secondary: 18D50, 55P48

References

Publication

Received: 28 July 2008
Revised: 10 October 2008
Accepted: 13 October 2008
Published: 12 November 2008

Authors