A formula for Stiefel-Whitney homology classes

Goldstein, Richard Z.; Turner, Edward C.

doi:10.1090/S0002-9939-1976-0415643-5

A formula for Stiefel-Whitney homology classes
HTML articles powered by AMS MathViewer

by Richard Z. Goldstein and Edward C. Turner PDF

Proc. Amer. Math. Soc. 58 (1976), 339-342 Request permission

Abstract:

The purpose of this paper is to define for $\bmod 2$ Euler spaces a formula which enables one to compute the Stiefel-Whitney homology classes in the original triangulation without passing to the first barycentric subdivision.

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
Thomas F. Banchoff, Stiefel-Whitney homology classes and singularities ofprojections for polyhedral manifolds, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Stanford Univ., Stanford, Calif., 1973) Amer. Math. Soc., Providence, R.I., 1975, pp. 333–347. MR 0377921
Richard Z. Goldstein, A Wu formula for Euler $\textrm {mod}$ $2$ spaces, Compositio Math. 32 (1976), no. 1, 33–39. MR 400251
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
Clint McCrory, Euler singularities and homology operations, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Part 1, Stanford Univ., Stanford, Calif., 1973) Amer. Math. Soc., Providence, R.I., 1975, pp. 371–380. MR 0377920
John W. Milnor and James D. Stasheff, Characteristic classes, Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. MR 0440554
N. E. Steenrod, Products of cocycles and extensions of mappings, Ann. of Math. (2) 48 (1947), 290–320. MR 22071, DOI 10.2307/1969172
D. Sullivan, Combinatorial invariants of analytic spaces, Proceedings of Liverpool Singularities—Symposium, I (1969/70), Lecture Notes in Mathematics, Vol. 192, Springer, Berlin, 1971, pp. 165–168. MR 0278333