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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2024 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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MathSciNet review: 1568075
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Kevin Walker
Title: An extension of Casson's invariant
Additional book information: Princeton University Press, Princeton, NJ, 1992, v+131 pp., US$16.50. ISBN 0-691-02532-0.

References [Enhancements On Off] (What's this?)

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  • Steven Boyer and Daniel Lines, Surgery formulae for Casson’s invariant and extensions to homology lens spaces, J. Reine Angew. Math. 405 (1990), 181–220. MR 1041002
  • S. Boyer and A. Nicas, Varieties of group representations and Casson’s invariant for rational homology $3$-spheres, Trans. Amer. Math. Soc. 322 (1990), no. 2, 507–522. MR 972701, DOI 10.1090/S0002-9947-1990-0972701-6
  • Sylvain E. Cappell, Ronnie Lee, and Edward Y. Miller, A symplectic geometry approach to generalized Casson’s invariants of $3$-manifolds, Bull. Amer. Math. Soc. (N.S.) 22 (1990), no. 2, 269–275. MR 1016041, DOI 10.1090/S0273-0979-1990-15885-9
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    C. L. Curtis-Budka, Casson-type invariants counting representations in low-rank groups, Doctoral thesis, Yale Univ. (1991).
  • Andreas Floer, An instanton-invariant for $3$-manifolds, Comm. Math. Phys. 118 (1988), no. 2, 215–240. MR 956166
  • P. B. Kronheimer, M. J. Larsen, and J. Scherk, Casson’s invariant and quadratic reciprocity, Topology 30 (1991), no. 3, 335–338. MR 1113682, DOI 10.1016/0040-9383(91)90018-Y
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    Invariant de Casson-Walker des spheres d'homologie rationelle fibrees de Seifert, C. R. Acad. Sci. Paris Sér. I Math. (1990), 727-730.
  • Christine Lescop, Un algorithme pour calculer l’invariant de Walker, Bull. Soc. Math. France 118 (1990), no. 3, 363–376 (French, with English summary). MR 1078081
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    Sur l'invariant de Casson-Walker: Formule de chirurgie globale et generalisation aux varietes de dimension 3 fermees orintees, C. R. Acad. Sci. Paris Sér. I Math. (1992), 437-440.
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    Global surgery formula for the Casson-Walker invariant, École Normale Superieure Lyon, preprint (May 1993).
  • Clifford Henry Taubes, Casson’s invariant and gauge theory, J. Differential Geom. 31 (1990), no. 2, 547–599. MR 1037415
  • Kevin Walker, An extension of Casson’s invariant to rational homology spheres, Bull. Amer. Math. Soc. (N.S.) 22 (1990), no. 2, 261–267. MR 1016040, DOI 10.1090/S0273-0979-1990-15883-5
    • Review Information:

    Reviewer: William M. Goldman
    Journal: Bull. Amer. Math. Soc. 30 (1994), 100-104
    DOI: https://doi.org/10.1090/S0273-0979-1994-00440-9