Bulletin (New Series) of the American Mathematical Society

A symplectic geometry approach to generalized Casson's invariants of 3-manifolds

Sylvain E. Cappell, Ronnie Lee, and Edward Y. Miller

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Bull. Amer. Math. Soc. (N.S.), Volume 22, Number 2 (1990), 269-275.

First available in Project Euclid: 4 July 2007

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Primary: 20C99: None of the above, but in this section
Secondary: 57M99: None of the above, but in this section


Cappell, Sylvain E.; Lee, Ronnie; Miller, Edward Y. A symplectic geometry approach to generalized Casson's invariants of 3-manifolds. Bull. Amer. Math. Soc. (N.S.) 22 (1990), no. 2, 269--275. https://projecteuclid.org/euclid.bams/1183555621

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  • [AM] S. Akbulut and J. McCarthy, Casson's invariant for oriented homology 3-spheres (to appear in Princeton math. notes).
  • [AMM] J. Arms, J. Marsden, and V. Moncrief, Symmetry and bifurcation of momentum mappings, Comm. Math. Phys. 78 (1981), 455-478.
  • [A] M. Atiyah, New invariants of three and four dimensional manifolds, Symposium on the Mathematical Heritage of Hermann Weyl, (R. Wells et al., eds.), Vol. 48, (1988) pp. 288-294.
  • [AB] M. Atiyah and R. Bott, The Yang-Mills equations over a Riemann surface, Philos. Trans. Roy. Soc. London 308 (1987), 523-615.
  • [B 1] E. Bierstone, Equivariant Gromov theory, Topology 13 (1974), 327-345.
  • [B 2] E. Bierstone, General position of equivariant maps, Trans. Amer. Math. Soc. 234 (1977), 447-466.
  • [BF] J.-M. Bismut and D. S. Freed, The analysis of elliptic families, I, Metrics and connections on determinant bundles, Commun. Math. Phys. 106 (1986), 159-176.
  • [BL] S. Boyer and D. Lines, Surgery formulae for Casson's invariant and extensions to homology lens spaces, in Rapport de recherches, Université du Québec à Montréal, 1988 (66).
  • [BN] S. Boyer and A. Nicas, Varieties of group representations and Casson's invariant for rational homology 3-spheres (preprint).
  • [E] J. Eliashberg, Cobordisme de solutions de relations différentielles, in Géométrie symplectique et de contact (D. Dazord and N. Desolneux-Morilis, eds.), Hermann, 1983, pp. 17-31.
  • [G] W. Goldman, The symplectic nature of the fundamental groups of surfaces, Adv. Math. 54 (1984), 200-225.
  • [J] D. Johnson, A geometric form of Casson's invariant and its connection to Reidemeister torsion (preprint).
  • [K] F. Kirwan, On the homology of compactifications of moduli spaces of vector bundles over Riemann surfaces, Proc. London Math. Soc. 53 (1986), 235-266.
  • [L] J. Alexander Lees, On the classification of Lagrange immersions, Duke Math. J. 43 (1976), 217-224.
  • [V] I. Vaisman, Symplectic geometry and secondary characteristic classes, in Progress in Mathematics, Vol. 72, Birkhäuser, Boston-Basel, 1987.
  • [W] K. Walker, An extension of Casson's invariant for rational homology spheres, this issue and Ph.D. thesis at Berkeley, 1989.
  • [Wi] E. Witten, Topological quantum field theory, preprint I.A.S., 1988.