Marked tubes and the graph multiplihedron

Details Marked tubes and the graph multiplihedron Marked tubes and the graph multiplihedron

2008-07-25

arxiv.org/abs/0807.4159v1

Algebraic and Geometric Topology 8 (2008) 2081-2108

Mathematics

Quantum Algebra

23 pages, 17 figures

Scientific paper

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 multiphihedron, 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.

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