## Algebraic & Geometric Topology

### Marked tubes and the graph multiplihedron

#### 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.

#### Article information

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

Dates
Revised: 10 October 2008
Accepted: 13 October 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796926

Digital Object Identifier
doi:10.2140/agt.2008.8.2081

Mathematical Reviews number (MathSciNet)
MR2460880

Zentralblatt MATH identifier
1160.52007

#### Citation

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. https://projecteuclid.org/euclid.agt/1513796926

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