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Article

Zhou, Jianwei
A note on characteristic classes. (English). Czechoslovak Mathematical Journal, vol. 56 (2006), issue 2, pp. 721-732
MSC: 53C05, 53C07, 55R25, 57R20 | MR 2291770 | Zbl 1164.53334
Keywords:
fibre bundle; characteristic class; transgression; Poincaré dual
Summary:
This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.
References:
[1] R.  Bott, L.  Tu: Differential Forms in Algebraic Topology. Springer GTM 82, , 1982. MR 0658304 | Zbl 0496.55001
[2] S. S.  Chern: A simple intrinsic proof of the Gauss-Bonnet formula for the closed Riemannian manifolds. Ann. Math. 45 (1944), 747–752. DOI 10.2307/1969302 | MR 0011027
[3] S. S.  Chern: On the curvature integral in a Riemannian manifold. Ann. Math. 46 (1945), 674–648. DOI 10.2307/1969203 | MR 0014760 | Zbl 0060.38104
[4] S. S.  Chern: Characteristic classes of Riemannian manifolds. Ann. Math. 47 (1946), 85–121. DOI 10.2307/1969037 | MR 0015793
[5] S. S.  Chern: On curvature and characteristic classes of a Riemannian manifold. Abh. Math. Sem. Univ. Hamburg 20 (1955), 117–162. DOI 10.1007/BF02960745 | MR 0075647
[6] P.  Griffiths, J.  Harris: Principles of Algebraic Geometry. Wiley-Interscience, New York, 1978. MR 0507725
[7] S. Kobayashi, K.  Nomizu: Foundations of Differential Geometry, Vol.  2. Interscience Publishers, New York, 1969.
[8] H. B.  Lawson, H.  Michelsohn: Spin Geometry. Princeton University Press, Princeton, 1989. MR 1031992
[9] V.  Mathai, D.  Quillen: Superconnections, Thom classes and equivariant differential forms. Topology 25 (1986), 85–110. DOI 10.1016/0040-9383(86)90007-8 | MR 0836726
[10] J.  W.  Milnor, J. D.  Stasheff: Characteristic Classes. Ann. of Math. Studies, No.  76. Princeton University Press, Princeton, 1974. MR 0440554
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