Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 8, Number 4 (2008), 2081-2108.
Marked tubes and the graph multiplihedron
Given a graph , we construct a convex polytope whose face poset is based on marked subgraphs of . 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.
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
Permanent link to this document
Digital Object Identifier
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]
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