Necessary and sufficient conditions for homotopy classification by cohomology and homotopy homomorphisms
Author:
Martin Sternstein
Journal:
Proc. Amer. Math. Soc. 34 (1972), 250-256
MSC:
Primary 55D15
DOI:
https://doi.org/10.1090/S0002-9939-1972-0296942-3
MathSciNet review:
0296942
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Abstract | References | Similar Articles | Additional Information
Abstract: Using obstruction theory tools to a pair of spaces two invariants are defined whose vanishing is a necessary and sufficient condition for homotopy classification of certain maps between these spaces by the induced cohomology and homotopy homomorphisms respectively.
- Donald W. Kahn, Maps which induce the zero map on homotopy, Pacific J. Math. 15 (1965), 537–540. MR 184232
- Katuhiko Mizuno, Semi cubical theory on higher obstruction, J. Inst. Polytech. Osaka City Univ. Ser. A 11 (1960), 15–22. MR 123327
- Paul Olum, Obstructions to extensions and homotopies, Ann. of Math. (2) 52 (1950), 1–50. MR 36507, DOI https://doi.org/10.2307/1969510 ---, Lecture notes from obstruction theory seminar, Cornell University, Ithaca, N.Y., 1968.
- Paul Olum, Factorizations and induced homomorphisms, Advances in Math. 3 (1969), 72–100. MR 238314, DOI https://doi.org/10.1016/0001-8708%2869%2990003-6
- Franklin P. Peterson, Some remarks on Chern classes, Ann. of Math. (2) 69 (1959), 414–420. MR 102807, DOI https://doi.org/10.2307/1970191 M. Sternstein, Ph.D. Dissertation, Cornell University, Ithaca, N.Y., 1971.
- Emery Thomas, Homotopy classification of maps by cohomology homomorphisms, Trans. Amer. Math. Soc. 111 (1964), 138–151. MR 160212, DOI https://doi.org/10.1090/S0002-9947-1964-0160212-4
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Additional Information
Keywords:
Posnikov decomposition,
<I>k</I>-invariant,
higher order cohomology operation,
obstruction
Article copyright:
© Copyright 1972
American Mathematical Society