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)

 
 

 

A combinatorial formula for normal Stiefel-Whitney classes


Authors: T. Banchoff and C. McCrory
Journal: Proc. Amer. Math. Soc. 76 (1979), 171-177
MSC: Primary 57R20
DOI: https://doi.org/10.1090/S0002-9939-1979-0534413-3
MathSciNet review: 534413
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

  • [1] T. Banchoff, Integral normal classes for polyhedral surfaces in 4-space (to appear).
  • [2] -, Stiefel-Whitney homology classes and singularities of projections for polyhedral manifolds, Proc. Sympos. Pure Math., vol. 27, Amer. Math. Soc., Providence, R. I., 1975, pp. 333-347. MR 0377921 (51:14090)
  • [3] R. Goldstein and E. Turner, A formula for Stiefel-Whitney homology classes, Proc. Amer. Math. Soc. 58 (1976), 339-342. MR 0415643 (54:3724)
  • [4] S. Halperin and D. Toledo, Stiefel-Whitney homology classes, Ann. of Math. (2) 96 (1972), 511-525. MR 0312515 (47:1072)
  • [5] R. Hardt and C. McCrory, Steenrod operations in subanalytic homology, Compositio Math. (to appear). MR 550647 (82b:55019)
  • [6] N. Levitt and C. Rourke, The existence of combinatorial formulae for characteristic classes (to appear). MR 0494134 (58:13063)
  • [7] C. McCrory, Euler singularities and homology operations, Proc. Sympos. Pure Math., vol. 27, Amer. Math. Soc., Providence, R. I., 1975, pp. 371-380. MR 0377920 (51:14089)
  • [8] -, Geometric homology operations, Advances in Math. (to appear).
  • [9] C. McCrory, D. Damiano and J. Stormes, Lectures on homology operations, Brown University, Providence, R. I., 1977.
  • [10] A. Shapiro, Obstructions to the imbedding of a complex in a Euclidean space, Ann. of Math. (2) 66 (1957), 256-269. MR 0089410 (19:671a)
  • [11] N. Steenrod, Products of cocycles and extensions of mappings, Ann. of Math. (2) 48 (1947), 290-316. MR 0022071 (9:154a)

Similar Articles

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

Retrieve articles in all journals with MSC: 57R20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0534413-3
Keywords: Stiefel-Whitney class, combinatorial manifold, singularity cycle, homology operation
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society