Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An axiomatic proof of Stiefel's conjecture


Authors: John D. Blanton and Clint McCrory
Journal: Proc. Amer. Math. Soc. 77 (1979), 409-414
MSC: Primary 55R40; Secondary 57R20
DOI: https://doi.org/10.1090/S0002-9939-1979-0545605-1
MathSciNet review: 545605
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Stiefel's combinatorial formula for the Stiefel-Whitney homology classes of a smooth manifold is proved, by verifying that the classes defined by his formula satisfy axioms which characterize the Stiefel-Whitney classes.


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

  • [1] E. Akin, Stiefel-Whitney homology classes and bordism, Trans. Amer. Math. Soc. 205 (1975), 341-359. MR 0358829 (50:11288)
  • [2] J. Blanton and P. Schweitzer, S.J., Axioms for characteristic classes of manifolds, Proc. Sympos. Pure Math., vol. 27, Amer. Math. Soc., Providence, R. I., 1975, pp. 436-443. MR 0375339 (51:11534)
  • [3] J. Cheeger, A combinatorial formula for Stiefel-Whitney classes, Topology of Manifolds, J. C. Cantrell and C. H. Edwards (eds.), Markham Publishing Co., Chicago, Ill., 1970, pp. 470-471.
  • [4] R. Goldstein and E. C. Turner, Stiefel-Whitney homology classes of quasi-regular cell complexes, Proc. Amer. Math. Soc. 64 (1977), 157-162. MR 0467765 (57:7617)
  • [5] S. Halperin and D. Toledo, Stiefel-Whitney homology classes, Ann. of Math. 96 (1972), 511-525. MR 0312515 (47:1072)
  • [6] -, The product formula for Stiefel-Whitney homology classes, Proc. Amer. Math. Soc. 48 (1975), 239-244. MR 0365584 (51:1836)
  • [7] E. Stiefel, Richtungsfelder und Fernparallelismus in n-dimensonalen Manigfaltigkeiten, Comment. Math. Helv. 8 (1936), 305-353. MR 1509530
  • [8] L. Taylor, Stiefel-Whitney homology classes, Quart. J. Math. Oxford Ser. (2) 28 (1977), 381-387. MR 0515729 (58:24286)
  • [9] H. Whitney, On the theory of sphere bundles, Proc. Nat. Acad. Sci. U.S.A. 26 (1940), 148-153. MR 0001338 (1:220b)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55R40, 57R20

Retrieve articles in all journals with MSC: 55R40, 57R20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0545605-1
Keywords: Stiefel-Whitney class, $ {C^\infty }$ manifold, triangulation, barycentric subdivision
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society