Complexes of connected graphs
Combinatorics
2014-09-23 v1 Geometric Topology
Abstract
Graphs with 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 theory, higher Chern-Simons theory and complexity theory.
Keywords
Cite
@article{arxiv.1409.5999,
title = {Complexes of connected graphs},
author = {V. A. Vassiliev},
journal= {arXiv preprint arXiv:1409.5999},
year = {2014}
}