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)



Stiefel-Whitney homology classes of quasi-regular cell complexes

Authors: Richard Goldstein and Edward C. Turner
Journal: Proc. Amer. Math. Soc. 64 (1977), 157-162
MSC: Primary 57D20; Secondary 57C05
MathSciNet review: 0467765
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A quasi-regular cell complex is defined and shown to have a reasonable barycentric subdivision. In this setting, Whitney's theorem that the k-skeleton of the barycentric subdivision of a triangulated n-manifold is dual to the $ (n - k)$th Stiefel-Whitney cohomology class is proven, and applied to projective spaces, lens spaces and surfaces.

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

  • 1. Ronald Brown, Elements of modern topology, McGraw-Hill, New York, 1968. MR 37 #3563. MR 0227979 (37:3563)
  • [M] M. Cohen, A course in simple homotopy theory, Springer-Verlag, Berlin and New York, 1973. MR 50 #14762. MR 0362320 (50:14762)
  • [S] Halperin and D. Toledo, Stiefel-Whitney homology classes, Ann. of Math. (2) 96 (1972), 511-525. MR 47 #1072. MR 0312515 (47:1072)
  • [P] J. Hilton and S. Wiley, Homology theory, Cambridge Univ. Press, New York, 1960. MR 22 #5963.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57D20, 57C05

Retrieve articles in all journals with MSC: 57D20, 57C05

Additional Information

Keywords: Euler $ \pmod 2$ space, Stiefel-Whitney homology class
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society