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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: 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.
- [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)
- [BLSWZ]
- A. Björner, M. Las Vergnas, B. Sturmfels, N. White, and G. Ziegler, Oriented matroids, Encyclopedia Math. Appl., Cambridge Univ. Press, 1992.
- [C]
- J. Cheeger, Spectral geometry of singular Riemannian spaces, J. Differential Geom. 18 (1983), 575-657. MR 730920 (85d:58083)
- [GGL]
- I. Gabrielov, I. Gelfand, and M. Losik, Combinatorial calculation of characteristic classes, Funktsional Anal, i Prilozhen. 9 (1975), 54-55; no. 2, 12-28; no. 3, 5-26. MR 0410758 (53:14504a)
- [M]
- R. MacPherson, The combinatorial formula of Garielov, Gelfand, and Loskik for the first Pontrjagin class, Séminaire Bourbaki No. 497, Lecture Notes in Math. vol. 667 Springer, Heidelburg, 1977. MR 521763 (81a:57022)
- [N]
- N. Levitt, Grassmannians and gauss maps in piecewise-linear topology, Lecture Notes in Math., vol. 1366, Springer, Heidelburg, 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
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