A combinatorial formula for normal Stiefel-Whitney classes

Banchoff, T.; McCrory, C.

doi:10.1090/S0002-9939-1979-0534413-3

A combinatorial formula for normal Stiefel-Whitney classes
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by T. Banchoff and C. McCrory

Proc. Amer. Math. Soc. 76 (1979), 171-177

DOI: https://doi.org/10.1090/S0002-9939-1979-0534413-3

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Abstract:

Using an ordering of the vertices of a combinatorial n-manifold K, we give an explicit description of a simplicial $\bmod 2$ cycle ${c_{n - i}}(K)$ which represents the dual of the ith normal Stiefel-Whitney class of K.

References

Integral normal classes for polyhedral surfaces in 4-space

Thomas F. Banchoff, Stiefel-Whitney homology classes and singularities ofprojections for polyhedral manifolds, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Part 1, Stanford Univ., Stanford, Calif., 1973) Amer. Math. Soc., Providence, R.I., 1975, pp. 333–347. MR 0377921
Richard Z. Goldstein and Edward C. Turner, A formula for Stiefel-Whitney homology classes, Proc. Amer. Math. Soc. 58 (1976), 339–342. MR 415643, DOI 10.1090/S0002-9939-1976-0415643-5
Stephen Halperin and Domingo Toledo, Stiefel-Whitney homology classes, Ann. of Math. (2) 96 (1972), 511–525. MR 312515, DOI 10.2307/1970823
Robert M. Hardt and Clint G. McCrory, Steenrod operations in subanalytic homology, Compositio Math. 39 (1979), no. 3, 333–371. MR 550647
Norman Levitt and Colin Rourke, The existence of combinatorial formulae for characteristic classes, Trans. Amer. Math. Soc. 239 (1978), 391–397. MR 494134, DOI 10.1090/S0002-9947-1978-0494134-6
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

Geometric homology operations

Lectures on homology operations

Arnold Shapiro, Obstructions to the imbedding of a complex in a euclidean space. I. The first obstruction, Ann. of Math. (2) 66 (1957), 256–269. MR 89410, DOI 10.2307/1969998
N. E. Steenrod, Products of cocycles and extensions of mappings, Ann. of Math. (2) 48 (1947), 290–320. MR 22071, DOI 10.2307/1969172