An axiomatic proof of Stiefel’s conjecture

Blanton, John D.; McCrory, Clint

doi:10.1090/S0002-9939-1979-0545605-1

An axiomatic proof of Stiefel’s conjecture
HTML articles powered by AMS MathViewer

by John D. Blanton and Clint McCrory

Proc. Amer. Math. Soc. 77 (1979), 409-414

DOI: https://doi.org/10.1090/S0002-9939-1979-0545605-1

PDF | Request permission

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

Ethan Akin, Stiefel-Whitney homology classes and bordism, Trans. Amer. Math. Soc. 205 (1975), 341–359. MR 358829, DOI 10.1090/S0002-9947-1975-0358829-4
John D. Blanton and Paul A. Schweitzer, Axioms for characteristic classes of manifolds, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Part 1, Stanford Univ., Stanford, Calif., 1973) Amer. Math. Soc., Providence, R.I., 1975, pp. 349–356. MR 0375339

A combinatorial formula for Stiefel-Whitney classes

Richard Goldstein and Edward C. Turner, Stiefel-Whitney homology classes of quasi-regular cell complexes, Proc. Amer. Math. Soc. 64 (1977), no. 1, 157–162. MR 467765, DOI 10.1090/S0002-9939-1977-0467765-1
Stephen Halperin and Domingo Toledo, Stiefel-Whitney homology classes, Ann. of Math. (2) 96 (1972), 511–525. MR 312515, DOI 10.2307/1970823
Stephen Halperin and Domingo Toledo, The product formula for Stiefel-Whitney homology classes, Proc. Amer. Math. Soc. 48 (1975), 239–244. MR 365584, DOI 10.1090/S0002-9939-1975-0365584-6
E. Stiefel, Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten, Comment. Math. Helv. 8 (1935), no. 1, 305–353 (German). MR 1509530, DOI 10.1007/BF01199559
Laurence R. Taylor, Stiefel-Whitney homology classes, Quart. J. Math. Oxford Ser. (2) 28 (1977), no. 112, 381–387. MR 515729, DOI 10.1093/qmath/28.4.381
Hassler Whitney, On the theory of sphere-bundles, Proc. Nat. Acad. Sci. U.S.A. 26 (1940), 148–153. MR 1338, DOI 10.1073/pnas.26.2.148