Nonstable homotopy groups of Thom complexes
HTML articles powered by AMS MathViewer
- by P. J. Ledden
- Proc. Amer. Math. Soc. 29 (1971), 404-410
- DOI: https://doi.org/10.1090/S0002-9939-1971-0288776-X
- PDF | Request permission
Abstract:
The first nonstable homotopy group of $MO(n),{\pi _{2n}}(MO(n))$, is computed for all n, together with the corresponding Postnikov invariant. The computations give a new proof of a theorem of Mahowald on the normal bundle of an imbedding.References
- René Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17–86 (French). MR 61823, DOI 10.1007/BF02566923
- Jean-Pierre Serre, Cohomologie modulo $2$ des complexes d’Eilenberg-MacLane, Comment. Math. Helv. 27 (1953), 198–232 (French). MR 60234, DOI 10.1007/BF02564562
- J. H. C. Whitehead, On simply connected, $4$-dimensional polyhedra, Comment. Math. Helv. 22 (1949), 48–92. MR 29171, DOI 10.1007/BF02568048
- Mark Mahowald, On the normal bundle of a manifold, Pacific J. Math. 14 (1964), 1335–1341. MR 176485
- W. S. Massey, Pontryagin squares in the Thom space of a bundle, Pacific J. Math. 31 (1969), 133–142. MR 250332 P. J. Ledden, Thom spaces, projective spaces, and a theorem of Whitney, Thesis, Stanford University, Stanford, Calif., 1965.
- W. S. Massey, On the Stiefel-Whitney classes of a manifold, Amer. J. Math. 82 (1960), 92–102. MR 111053, DOI 10.2307/2372878
- W. S. Massey, Proof of a conjecture of Whitney, Pacific J. Math. 31 (1969), 143–156. MR 250331
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 404-410
- MSC: Primary 57.20
- DOI: https://doi.org/10.1090/S0002-9939-1971-0288776-X
- MathSciNet review: 0288776