| Title:
|
A note on characteristic classes (English) |
| Author:
|
Zhou, Jianwei |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
721-732 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
fibre bundle |
| Keyword:
|
characteristic class |
| Keyword:
|
transgression |
| Keyword:
|
Poincaré dual |
| MSC:
|
53C05 |
| MSC:
|
53C07 |
| MSC:
|
55R25 |
| MSC:
|
57R20 |
| idZBL:
|
Zbl 1164.53334 |
| idMR:
|
MR2291770 |
| . |
| Date available:
|
2009-09-24T11:37:27Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128100 |
| . |
| Reference:
|
[1] R. Bott, L. Tu: Differential Forms in Algebraic Topology.Springer GTM 82, , 1982. Zbl 0496.55001, MR 0658304 |
| Reference:
|
[2] S. S. Chern: A simple intrinsic proof of the Gauss-Bonnet formula for the closed Riemannian manifolds.Ann. Math. 45 (1944), 747–752. MR 0011027, 10.2307/1969302 |
| Reference:
|
[3] S. S. Chern: On the curvature integral in a Riemannian manifold.Ann. Math. 46 (1945), 674–648. Zbl 0060.38104, MR 0014760, 10.2307/1969203 |
| Reference:
|
[4] S. S. Chern: Characteristic classes of Riemannian manifolds.Ann. Math. 47 (1946), 85–121. MR 0015793, 10.2307/1969037 |
| Reference:
|
[5] S. S. Chern: On curvature and characteristic classes of a Riemannian manifold.Abh. Math. Sem. Univ. Hamburg 20 (1955), 117–162. MR 0075647, 10.1007/BF02960745 |
| Reference:
|
[6] P. Griffiths, J. Harris: Principles of Algebraic Geometry.Wiley-Interscience, New York, 1978. MR 0507725 |
| Reference:
|
[7] S. Kobayashi, K. Nomizu: Foundations of Differential Geometry, Vol. 2.Interscience Publishers, New York, 1969. |
| Reference:
|
[8] H. B. Lawson, H. Michelsohn: Spin Geometry.Princeton University Press, Princeton, 1989. MR 1031992 |
| Reference:
|
[9] V. Mathai, D. Quillen: Superconnections, Thom classes and equivariant differential forms.Topology 25 (1986), 85–110. MR 0836726, 10.1016/0040-9383(86)90007-8 |
| Reference:
|
[10] J. W. Milnor, J. D. Stasheff: Characteristic Classes. Ann. of Math. Studies, No. 76.Princeton University Press, Princeton, 1974. MR 0440554 |
| . |
