Stiefel-Whitney homology classes of quasi-regular cell complexes
HTML articles powered by AMS MathViewer
- by Richard Goldstein and Edward C. Turner
- Proc. Amer. Math. Soc. 64 (1977), 157-162
- DOI: https://doi.org/10.1090/S0002-9939-1977-0467765-1
- PDF | Request permission
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
- Ronald Brown, Elements of modern topology, McGraw-Hill Book Co., New York-Toronto-London, 1968. MR 0227979
- Marshall M. Cohen, A course in simple-homotopy theory, Graduate Texts in Mathematics, Vol. 10, Springer-Verlag, New York-Berlin, 1973. MR 0362320
- Stephen Halperin and Domingo Toledo, Stiefel-Whitney homology classes, Ann. of Math. (2) 96 (1972), 511–525. MR 312515, DOI 10.2307/1970823 J. Hilton and S. Wiley, Homology theory, Cambridge Univ. Press, New York, 1960. MR 22 #5963.
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 64 (1977), 157-162
- MSC: Primary 57D20; Secondary 57C05
- DOI: https://doi.org/10.1090/S0002-9939-1977-0467765-1
- MathSciNet review: 0467765