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Transactions of the American Mathematical Society

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Stiefel-Whitney homology classes and bordism


Author: Ethan Akin
Journal: Trans. Amer. Math. Soc. 205 (1975), 341-359
MSC: Primary 57D90
DOI: https://doi.org/10.1090/S0002-9947-1975-0358829-4
MathSciNet review: 0358829
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Abstract: We develop the theory of $ \bmod 2$ Stiefel-Whitney homology classes for Euler polyhedra. We then describe a simple method of obtaining p.1. bordism theories. Finally, we define the ungraded bordism theory of Euler spaces and show that it is isomorphic to ordinary total homology.


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

  • [A$ _{1}$] E. Akin, Manifold phenomena in the theory of polyhedra, Trans. Amer. Math. Soc. 143 (1969), 413-473. MR 40 #6544. MR 0253329 (40:6544)
  • [A$ _{2}$] -, Transverse cellular mappings of polyhedra, Trans. Amer. Math. Soc. 169 (1972), 401-438. MR 0326745 (48:5088)
  • [C] M. Cohen, A general theory of relative regular neighborhoods, Trans. Amer. Math. Soc. 136 (1969), 189-229. MR 40 #2052. MR 0248802 (40:2052)
  • [C-F] P. Conner and E. E. Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Bd. 33, Academic Press, New York; Springer-Verlag, Berlin, 1964. MR 31 #750. MR 0176478 (31:750)
  • [Ch] G. Cheeger, A combinatorial formula for Steifel-Whitney classes Topology of Manifolds (J. C. Cantrell and C. H. Edwards Editors), Markham, Chicago, Ill., 1971.
  • [G] L. C. Glaser, Geometrical combinatorial topology, Vol. 1, Van Nostrand Reinhold, Princeton, N. J., 1970.
  • [H-T] S. Halperin and D. Toledo, Stiefel-Whitney homology classes, Ann. of Math. (2) 96 (1972), 511-525. MR 47 #1072. MR 0312515 (47:1072)
  • [S] D. Sullivan, Combinatorial invariants of analytic spaces, Proc. Liverpool Singularities-Symposium I, Lecture Notes in Math, no. 192, Springer-Verlag, New York, 1971. MR 0278333 (43:4063)

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DOI: https://doi.org/10.1090/S0002-9947-1975-0358829-4
Article copyright: © Copyright 1975 American Mathematical Society

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