[109] Configuration Spaces and Imbedding Problems

  • Raoul Bott
Part of the Contemporary Mathematicians book series (CM)

The purpose of this talk is to present joint work with Clifford Taubes on a purely topological approach towards the recent physics-inspired self-linking invariants for knots described by Dror Bar-Natan [2] and Guadagnini, Martinelli, and Mintchev [5] . As I hope to show, the configuration spaces and their natural compactifications à la Fulton and MacPherson [4] are precisely the needed ingredients to explain these invariants and their generalizations.

DEFINITION 1. Let Z be a topological space. The configuration space of n points in Z, \(C_n^0\left( Z \right)\)


  1. R. Bott, Configuration spaces and imbedding invariants, to be published in the Gokova Topology Conference, 1995.Google Scholar
  2. D. Bar-Natan, Pertubative aspects of the Chern-Simon topological quantum field theory, Ph.D. Thesis, Princeton University, 1991; On the Vassiliev knot invariants, Topology 34 (1995), 423-472.Google Scholar
  3. R. Bott and C. Taubes, On the self-linking of knots, J. Math. Phys. 35 (1994), 5247-5287.MathSciNetCrossRefGoogle Scholar
  4. W. Fulton and R. MacPherson, Compactification of configuration spaces, Annals of Math. 139 (1994), 183-225.MathSciNetCrossRefGoogle Scholar
  5. E. Guadagnini, M. Martinelli and M. Mintchev, Pertubative aspects of the Chem-Simons field theory, Phys. Lett. B227 (1989), 111-117.CrossRefGoogle Scholar
  6. Wu Wen-Tsun, A theory of imbedding, immersion, and isotopy of polytopes in a Euclidean space (1965), Peking, Scientific Press.zbMATHGoogle Scholar

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Authors and Affiliations

  • Raoul Bott
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

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