Marked tubes and the graph multiplihedron

Devadoss, Satyan¹ ; Forcey, Stefan²

¹Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, USA
²Department of Physics and Mathematics, Tennessee State University, Nashville, TN 37209, USA

Algebraic and Geometric Topology, Tome 8 (2008) no. 4, pp. 2081-2108

Résumé

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.

Détail

DOI : 10.2140/agt.2008.8.2081

Keywords: multiplihedron, graph associahedron, realization, convex hull

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