Correction to: βThe stable geometric dimension of vector bundles over real projective spacesβ [Trans. Amer. Math. Soc. 268 (1981), no. 1, 39β61; MR0628445 (83c:55006)]
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- by Donald M. Davis, Sam Gitler and Mark Mahowald PDF
- Trans. Amer. Math. Soc. 280 (1983), 841-843 Request permission
Abstract:
The theory of $bo$-resolutions as utilized in The stable geometric dimension of vector bundles over real projective spaces did not give adequate care to the $K{{\mathbf {Z}}_2}$βs occurring at each stage of the resolution. This restricts somewhat the set of integers $e$ for which we can prove that the geometric dimension of vector bundles of order ${2^e}$ on large real projective spaces is precisely $2 e + \delta$.References
- Donald M. Davis, The splitting of $B\textrm {O}\langle 8\rangle \wedge b\textrm {o}$ and $M\textrm {O}\langle 8\rangle \wedge b\textrm {o}$, Trans. Amer. Math. Soc. 276 (1983), no.Β 2, 671β683. MR 688969, DOI 10.1090/S0002-9947-1983-0688969-6
- Donald M. Davis, Sam Gitler, and Mark Mahowald, The stable geometric dimension of vector bundles over real projective spaces, Trans. Amer. Math. Soc. 268 (1981), no.Β 1, 39β61. MR 628445, DOI 10.1090/S0002-9947-1981-0628445-8
- Mark Mahowald, $b\textrm {o}$-resolutions, Pacific J. Math. 92 (1981), no.Β 2, 365β383. MR 618072, DOI 10.2140/pjm.1981.92.365 β, An addendum to $bo$-resolutions, Pacific J. Math. (to appear).
- Mark Mahowald, The image of $J$ in the $EHP$ sequence, Ann. of Math. (2) 116 (1982), no.Β 1, 65β112. MR 662118, DOI 10.2307/2007048
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 280 (1983), 841-843
- MSC: Primary 55N15; Secondary 55R25
- DOI: https://doi.org/10.1090/S0002-9947-1983-0716854-X
- MathSciNet review: 716854