Acta mathematica scientia, Series B >
COBORDISM CLASSES OF FIBERINGS OVER PRODUCT OF PROJECTIVE SPACES
Received date: 2006-12-16
Online published: 2009-09-20
Supported by
Project Supported by NSFC (10371029), HNSF (103144) and SRF for ROCS, SEM
Let RP(k) denote the k-dimensional real projective space. This article determines which cobordism classes are represented by the total space of a fibering with prescribed base space RP(3)\times RP(1), RP(2)×RP(1), RP(2)\times RP(1)×RP(1) or $RP(3)\times RP(2).
Key words： fibering; characteristic number; cobordism class
WANG Yan-Ying , LI Jing-Yan . COBORDISM CLASSES OF FIBERINGS OVER PRODUCT OF PROJECTIVE SPACES[J]. Acta mathematica scientia, Series B, 2009 , 29(5) : 1421 -1429 . DOI: 10.1016/S0252-9602(09)60114-4
[1] Conner P E. Differentiable Periodic Maps. Lecture Notes in Math 738. 2nd ed. Berlin, Heidelberg, New York: Springer-Verlag, 1979
[2] Stong R E. On fibering of cobordism classes. Trans Amer Math Soc, 1973, 178: 431--447
[3] Brown R L W. Cobordism and bundles over spheres. Michigan Math J, 1969, 16: 315--320
[4] O'Reilly D F X. Cobordism classes of fiber bundles. Pacific J Math, 1977, 69: 467--475
[5] Yang H J. Cobordism classes of fiber bundles. Chinese Sci Bull, 1990, 35: 1409--1413
[6] Wang Y Y. Characteristic numbers and cobordism class of fiberings with fiber RP(2k). Proc Amer Math Soc, 2000, 129: 899--911
[7] Borel A, Hirzebruch F. Characteristic classes and homogeneous space. Amer J Math, 1958, 80: 458--538
[8] Milnor J W, Stasheff J D. Characteristic Classes. Princeton, New Jersey: Princeton University Press and University of Tokyo Press, 1974
[9] Jiang Y F, Liu Z Z, Liu X B. Commuting involutions fixing isolated points. Acta Mathematica Scientia, 2004, 24A(1): 38--44 (in Chinese)
[10] Wang Y Y, Wang Y Y. Cobordism and fiber bundle. Acta Scientiarum Naturalium Universitates Nankaiensis, 2007, 40: 46--50
/
| 〈 |
|
〉 |