Diagonals on the permutahedra, multiplihedra and associahedra
By S. Saneblidze, R. Umble. 2002
106 citations recorded by the source corpus.
We construct an explicit diagonal on the permutahedra {Pn}. Related diagonals on the multiplihedra {Jn} and the associahedra {Kn} are induced by Tonks' projection θ : Pn → Kn+1 (19) and its factorization through Jn. We use the diagonal on {Kn} to define the tensor product ofA∞-(co)algebras. We introduce the notion of a permutahedral set Z, observe that the double cobar construction Ω 2 C∗ (X) is a naturally occurring example and lift the diagonal on {Pn} to a diagonal on Z.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a3169ae61a290e535df6ef8d21f07416d7ef2cf1
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A link surgery spectral sequence in monopole Floer homology (2009, background): “n each is naturally a renement of the hypercube (see Figure 17), and we may arrange that P n+1 renes K n+2 as well. Upon sharing these realizations with experts, we were directed to similar ones in [27], which also rene hypercubes but have vastly dierent origins. For K nas a convex hull, see [18] an”
- Convex Hull Realizations of the Multiplihedra (2007, background): “The largest pentagonal facet of this picture corresponds to the bottom pentagonal facet in the drawing of J (4) on page 53 of [36], and to the pentagonal facet labeled d(0,1) in the diagram of J (4) in section 5 of [33].”