Inadequacy of ordinary homology theory

Lin, T. Y.

doi:10.1090/S0002-9939-1972-0307241-5

Inadequacy of ordinary homology theory
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by T. Y. Lin

Proc. Amer. Math. Soc. 31 (1972), 617-619

DOI: https://doi.org/10.1090/S0002-9939-1972-0307241-5

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Abstract:

Counterexamples to the homology version of Peterson’s theorem are constructed. Namely, maps are exhibited which theoretically cannot be detected by any primary or higher order homology operations.

References

J. F. Adams, Lectures on generalised cohomology, Category Theory, Homology Theory and their Applications, III (Battelle Institute Conference, Seattle, Wash., 1968, Vol. Three), Springer, Berlin, 1969, pp. 1–138. MR 0251716
T. Y. Lin, Homological algebra of stable homotopy ring $\pi _{^{\ast } }$ of spheres, Pacific J. Math. 38 (1971), 117–143. MR 307233

Homological dimension of ${\pi _\ast }$-modules and their geometric characterizations

Peter Freyd, Stable homotopy, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 121–172. MR 0211399
Daniel M. Kan and George W. Whitehead, On the realizability of singular cohomology groups, Proc. Amer. Math. Soc. 12 (1961), 24–25. MR 123319, DOI 10.1090/S0002-9939-1961-0123319-6
Franklin P. Peterson, Functional cohomology operations, Trans. Amer. Math. Soc. 86 (1957), 197–211. MR 105679, DOI 10.1090/S0002-9947-1957-0105679-9