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.


Connected Graph Spectral Sequence Simplicial Complex Homology Group Braid Group 
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© Springer Science+Business Media New York 1993

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  • V. A. Vassiliev

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