Algebraic & Geometric Topology

Marked tubes and the graph multiplihedron

Satyan Devadoss and Stefan Forcey

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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.

Article information

Algebr. Geom. Topol., Volume 8, Number 4 (2008), 2081-2108.

Received: 28 July 2008
Revised: 10 October 2008
Accepted: 13 October 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 52B11: $n$-dimensional polytopes
Secondary: 18D50: Operads [See also 55P48] 55P48: Loop space machines, operads [See also 18D50]

multiplihedron graph associahedron realization convex hull


Devadoss, Satyan; Forcey, Stefan. Marked tubes and the graph multiplihedron. Algebr. Geom. Topol. 8 (2008), no. 4, 2081--2108. doi:10.2140/agt.2008.8.2081.

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