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Complexes of Connected Graphs

In: The Gelfand Mathematical Seminars, 1990–1992

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  • V. A. Vassiliev

Abstract

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.

Suggested Citation

  • V. A. Vassiliev, 1993. "Complexes of Connected Graphs," Springer Books, in: Israel M. Gelfand & Lawrence Corwin & James Lepowsky (ed.), The Gelfand Mathematical Seminars, 1990–1992, pages 223-235, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0345-2_15
    DOI: 10.1007/978-1-4612-0345-2_15
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