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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

A combinatorial formula for the Pontrjagin classes


Authors: I. M. GelЬfand and R. D. MacPherson
Journal: Bull. Amer. Math. Soc. 26 (1992), 304-309
MSC (2000): Primary 57R20; Secondary 05B35
MathSciNet review: 1129313
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Abstract | References | Similar Articles | Additional Information

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

  • [BLSWZ] A. Björner, M. Las Vergnas, B. Sturmfels, N. White, and G. Ziegler, Oriented matroids, Encyclopedia Math. Appl., Cambridge Univ. Press, 1992.
  • [C] Jeff Cheeger, Spectral geometry of singular Riemannian spaces, J. Differential Geom. 18 (1983), no. 4, 575–657 (1984). MR 730920 (85d:58083)
  • [GGL] 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 (53 #14504a)
  • [M] 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 (81a:57022)
  • [N] Norman Levitt, Grassmannians and Gauss maps in piecewise-linear topology, Lecture Notes in Mathematics, vol. 1366, Springer-Verlag, Berlin, 1989. MR 989273 (90e:57042)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1992-00282-3
PII: S 0273-0979(1992)00282-3
Article copyright: © Copyright 1992 American Mathematical Society