[110] Critical Point Theory in Mathematics and in Mathematical Physics

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


At last year’s Gökova Conference I reported on a “topological approach” to the “new” knot invariants, which ClifF Taubes and I had worked out along lines initiated by Axelrod and Singer [AS] and Kontsevich [K] in their work on 3-manifold invariants.


  1. Raoul Bott, Configuration spaces and Imbedding invariants, Turkish J. of Math. 20 No. 1 (1996) 1-17.Google Scholar
  2. Raoul Bott, Clifford Taubes, On the self-linking of knots, J. Math. Phys. 35 No. 10, (1994) 5247-5287.Google Scholar
  3. M. Kontsevich, Feynman diagrams and low-dimensional topology, Max Plank Institute Preprint, 1992.Google Scholar
  4. D. M. Austin, P.J. Braam, Morse-Dott theory and equivariant cohomology, The Floer Memorial Vol. Birkhauser, 1995.Google Scholar
  5. J. J. Duistermaat, G. J. Heckman, On the variation in the cohomology in the symplectic form of the reduced space, Invent. Math. 69 (1982) 259-268.Google Scholar
  6. Albert Schwarz, Quantum field theory and topology, Springer, 1993.Google Scholar
  7. S. Minakhsi-sundaram, A. Pleijel, Some properties of the eigenfuncttons of the Laplace operator on Riemannian manifolds, Can J. of Math. 1 (1949) 242-256.Google Scholar
  8. D. B. Ray, I. M. Singer, R-Torsion and the Laplacian on Riemannian manifolds, Advances in Math. 7 (1971) 145-210.Google Scholar
  9. Atiyah, Patodi, I. M. Singer, Spectral asymmetry and Riemann geometry: III, Math Proc. Camb. Phil. Soc. 79 (1976) 71-99.Google Scholar
  10. Scott Axelrod, I.M. Singer, Chern-Simons perturbation theory II, J. Diff. Geom. 39 (1994) 173-213.Google Scholar
  11. E. Witten, Quantum field theory and the Jones polynomial, Coramun. Math. Phys. 121 (1984) 351-399.Google Scholar
  12. S. S. Chern, James Simons, Some cohomology classes in principal fibre bundles and their application to Riemannian Geometry, Proc. Nas. 68 (1971) 791-794.Google Scholar
  13. S. S. Chern, James Simons, Characteristic forms and geometrie invariants, Ann. of Math. 99 (1974) 48-69.Google Scholar
  14. D. Bar-Natan, On the Vassiliev knot invariants, Topology 34 No. 2 (1995) 423-472.Google Scholar
  15. E. Guadagnini, M. Martellini, M. Mintchev, Perturbative aspects of Chern-Simons topological quantum field theory, Phys. Lett. B 227 (1989) 111.Google Scholar
  16. R. T. Seeley, Powers of an elliptic operator, A.M.S. Proc. Symp. Pure Math. 10 (1967), 288-307.Google Scholar

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Authors and Affiliations

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

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