Marked tubes and the graph multiplihedron

Devadoss, Satyan; Forcey, Stefan

doi:10.2140/agt.2008.8.2081

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Marked tubes and the graph multiplihedron

Satyan Devadoss and Stefan Forcey

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 2000

Primary: 52B11

Secondary: 18D50, 55P48

References

Publication

Received: 28 July 2008

Revised: 10 October 2008

Accepted: 13 October 2008

Published: 12 November 2008

Authors

Satyan Devadoss
Department of Mathematics and Statistics Williams College Williamstown, MA 01267 USA
http://www.williams.edu/mathematics/devadoss/
Stefan Forcey
Department of Physics and Mathematics Tennessee State University Nashville, TN 37209 USA
http://faculty.tnstate.edu/sforcey/

Volume 8, issue 4 (2008)