Complexes of Connected Graphs
By V. Vassiliev. 2014
57 citations recorded by the source corpus.
Graphs with the given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applications to the topology of braid groups, knot theory, combinatorics, and singularity theory. The multidimensional analogues of this complex are indicated, which arise naturally in the homotopy topology, higher dimensional Chern-Simons theory and complexity theory.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Spectroscopy
View Paper: https://www.semanticscholar.org/paper/1ebd35f42d81ada1bf6c808bc29a291861465a5c
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In Computational Theory and Mathematics
- Dmitry N. Kozlov
- Victor Tourtchine
- Michelle L. Wachs
- Matthew Kahle
- John Shareshian
- R. Gurau
- Vidit Nanda
- Konstantin Mischaikow
In Geometry and Topology
- Dmitry N. Kozlov
- Victor Tourtchine
- Michelle L. Wachs
- Victor Turchin
- Ryan Budney
- Matthew Kahle
- Eva Maria Feichtner
- R. Gurau
In Spectroscopy
Citations in the corpus
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- A simple proof for folds on both sides in complexes of graph homomorphisms (2004, result): “As a sample, it yields an extremely short proof of the fact that the complex of disconnected graphs is a strong deformation retract of the order complex of the partition lattice: the ascending closure operator takes each disconnected graph G to the partition, whose blocks are the connected component”
- Topology of matching, chessboard, and general bounded degree graph complexes (2003, background): “Whenk =1 ; 2, the complex arises in connection with Vassiliev knot invariants [ 47 , 48].”
- On the other side of the bialgebra of chord diagrams (2004, background): “he result of this gluing by minus 1. 2 Basis in the complexes CT∗D. Alternated T∗-diagrams 2.1 Basis in T− M, T + M There exist three different types of basis for these Z-modules: basis of snakes, cf. [35], basis of monotone trees and basis of alternated trees, cf. [30]. To define the first basis one n”