Orientability of manifolds for generalised homology theories

Orientability of manifolds for generalised homology theories
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by W. C. Hsiang and C. T. C. Wall PDF

Trans. Amer. Math. Soc. 118 (1965), 352-359 Request permission

References

M. F. Atiyah, Bordism and cobordism, Proc. Cambridge Philos. Soc. 57 (1961), 200–208. MR 126856, DOI 10.1017/s0305004100035064
M. F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous spaces, Proc. Sympos. Pure Math., Vol. III, American Mathematical Society, Providence, R.I., 1961, pp. 7–38. MR 0139181
M. F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology 3 (1964), no. suppl, suppl. 1, 3–38. MR 167985, DOI 10.1016/0040-9383(64)90003-5

Homotopy type of differentiable manifolds

Edgar H. Brown Jr., Cohomology theories, Ann. of Math. (2) 75 (1962), 467–484. MR 138104, DOI 10.2307/1970209

Relations between ordinary and extraordinary cohomology

Albrecht Dold, Partitions of unity in the theory of fibrations, Ann. of Math. (2) 78 (1963), 223–255. MR 155330, DOI 10.2307/1970341
James Eells Jr. and Nicolaas H. Kuiper, Manifolds which are like projective planes, Inst. Hautes Études Sci. Publ. Math. 14 (1962), 5–46. MR 145544
Samuel Eilenberg and Norman E. Steenrod, Axiomatic approach to homology theory, Proc. Nat. Acad. Sci. U.S.A. 31 (1945), 117–120. MR 12228, DOI 10.1073/pnas.31.4.117
Samuel Eilenberg and Norman Steenrod, Foundations of algebraic topology, Princeton University Press, Princeton, N.J., 1952. MR 0050886
Michel A. Kervaire, A manifold which does not admit any differentiable structure, Comment. Math. Helv. 34 (1960), 257–270. MR 139172, DOI 10.1007/BF02565940
J. M. Kister, Microbundles are fibre bundles, Bull. Amer. Math. Soc. 69 (1963), 854–857. MR 156359, DOI 10.1090/S0002-9904-1963-11064-2

Microbundles

J. Milnor, Topological manifolds and smooth manifolds, Proc. Internat. Congr. Mathematicians (Stockholm, 1962) Inst. Mittag-Leffler, Djursholm, 1963, pp. 132–138. MR 0161345
L. S. Pontryagin, Smooth manifolds and their applications in homotopy theory, American Mathematical Society Translations, Ser. 2, Vol. 11, American Mathematical Society, Providence, R.I., 1959, pp. 1–114. MR 0115178
Stephen Smale, Generalized Poincaré’s conjecture in dimensions greater than four, Ann. of Math. (2) 74 (1961), 391–406. MR 137124, DOI 10.2307/1970239
René Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17–86 (French). MR 61823, DOI 10.1007/BF02566923
C. T. C. Wall, Classification of $(n-1)$-connected $2n$-manifolds, Ann. of Math. (2) 75 (1962), 163–189. MR 145540, DOI 10.2307/1970425
George W. Whitehead, Generalized homology theories, Trans. Amer. Math. Soc. 102 (1962), 227–283. MR 137117, DOI 10.1090/S0002-9947-1962-0137117-6

Some aspects of stable homotopy theory