Complexes of Connected Graphs
Victor Anatolievich Vassiliev · Birkhäuser Boston eBooks · 1993
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. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.