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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 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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A combinatorial formula for the Pontrjagin classes
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by I. M. Gel′fand and R. D. MacPherson PDF
Bull. Amer. Math. Soc. 26 (1992), 304-309 Request permission

Abstract:

A combinatorial formula for the Pontrjagin classes of a triangulated manifold is given. The main ingredients are oriented matroid theory and a modified formulation of Chern-Weil theory.
References
    A. Björner, M. Las Vergnas, B. Sturmfels, N. White, and G. Ziegler, Oriented matroids, Encyclopedia Math. Appl., Cambridge Univ. Press, 1992.
  • Jeff Cheeger, Spectral geometry of singular Riemannian spaces, J. Differential Geom. 18 (1983), no. 4, 575–657 (1984). MR 730920
  • A. M. Gabrièlov, I. M. Gel′fand, and M. V. Losik, Combinatorial computation of characteristic classes. I, II, Funkcional. Anal. i Priložen. 9 (1975), no. 2, 12–28; ibid. 9 (1975), no. 3, 5–26 (Russian). MR 0410758
  • Robert MacPherson, The combinatorial formula of Gabrielov, Gel′fand and Losik for the first Pontrjagin class, Séminaire Bourbaki, 29e année (1976/77), Lecture Notes in Math., vol. 677, Springer, Berlin, 1978, pp. Exp. No. 497, pp. 105–124. MR 521763
  • Norman Levitt, Grassmannians and Gauss maps in piecewise-linear topology, Lecture Notes in Mathematics, vol. 1366, Springer-Verlag, Berlin, 1989. MR 989273, DOI 10.1007/BFb0084994
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 26 (1992), 304-309
  • MSC (2000): Primary 57R20; Secondary 05B35
  • DOI: https://doi.org/10.1090/S0273-0979-1992-00282-3
  • MathSciNet review: 1129313