Stiefel-Whitney homology classes and bordism

Akin, Ethan

doi:10.1090/S0002-9947-1975-0358829-4

Stiefel-Whitney homology classes and bordism
HTML articles powered by AMS MathViewer

by Ethan Akin PDF

Trans. Amer. Math. Soc. 205 (1975), 341-359 Request permission

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

Ethan Akin, Manifold phenomena in the theory of polyhedra, Trans. Amer. Math. Soc. 143 (1969), 413–473. MR 253329, DOI 10.1090/S0002-9947-1969-0253329-1
Ethan Akin, Transverse cellular mappings of polyhedra, Trans. Amer. Math. Soc. 169 (1972), 401–438. MR 326745, DOI 10.1090/S0002-9947-1972-0326745-7
Marshall M. Cohen, A general theory of relative regular neighborhoods, Trans. Amer. Math. Soc. 136 (1969), 189–229. MR 248802, DOI 10.1090/S0002-9947-1969-0248802-6
P. E. Conner and E. E. Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 33, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1964. MR 0176478

A combinatorial formula for Steifel-Whitney classes

Geometrical combinatorial topology

Stephen Halperin and Domingo Toledo, Stiefel-Whitney homology classes, Ann. of Math. (2) 96 (1972), 511–525. MR 312515, DOI 10.2307/1970823
D. Sullivan, Combinatorial invariants of analytic spaces, Proceedings of Liverpool Singularities—Symposium, I (1969/70), Lecture Notes in Mathematics, Vol. 192, Springer, Berlin, 1971, pp. 165–168. MR 0278333