Integral Brown-Gitler spectra
HTML articles powered by AMS MathViewer
- by Fred R. Cohen, Donald M. Davis, Paul G. Goerss and Mark E. Mahowald PDF
- Proc. Amer. Math. Soc. 103 (1988), 1299-1304 Request permission
Abstract:
A Thom spectrum model for integral Brown-Gitler spectra is established and shown to have a multiplicative property. This clarifies certain aspects of an earlier application to splitting $bo \wedge bo$.References
- A. K. Bousfield, The localization of spaces with respect to homology, Topology 14 (1975), 133–150. MR 380779, DOI 10.1016/0040-9383(75)90023-3
- Edgar H. Brown Jr. and Samuel Gitler, A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra, Topology 12 (1973), 283–295. MR 391071, DOI 10.1016/0040-9383(73)90014-1
- Frederick R. Cohen, Thomas J. Lada, and J. Peter May, The homology of iterated loop spaces, Lecture Notes in Mathematics, Vol. 533, Springer-Verlag, Berlin-New York, 1976. MR 0436146
- F. R. Cohen, J. P. May, and L. R. Taylor, $K(\textbf {Z},\,0)$ and $K(Z_{2},\,0)$ as Thom spectra, Illinois J. Math. 25 (1981), no. 1, 99–106. MR 602900
- Ralph L. Cohen, The immersion conjecture for differentiable manifolds, Ann. of Math. (2) 122 (1985), no. 2, 237–328. MR 808220, DOI 10.2307/1971304
- Ralph L. Cohen, The geometry of $\Omega ^{2}S^{3}$ and braid orientations, Invent. Math. 54 (1979), no. 1, 53–67. MR 549545, DOI 10.1007/BF01391176
- 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. 1, 39–61. MR 628445, DOI 10.1090/S0002-9947-1981-0628445-8
- Richard M. Kane, Operations in connective $K$-theory, Mem. Amer. Math. Soc. 34 (1981), no. 254, vi+102. MR 634210, DOI 10.1090/memo/0254
- Mark Mahowald, A new infinite family in ${}_{2}\pi _{*}{}^s$, Topology 16 (1977), no. 3, 249–256. MR 445498, DOI 10.1016/0040-9383(77)90005-2
- Mark Mahowald, $b\textrm {o}$-resolutions, Pacific J. Math. 92 (1981), no. 2, 365–383. MR 618072
- Mark Mahowald, Ring spectra which are Thom complexes, Duke Math. J. 46 (1979), no. 3, 549–559. MR 544245
- J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Vol. 347, Springer-Verlag, Berlin-New York, 1973. MR 0420609
- R. James Milgram, Iterated loop spaces, Ann. of Math. (2) 84 (1966), 386–403. MR 206951, DOI 10.2307/1970453
- Don H. Shimamoto, An integral version of the Brown-Gitler spectrum, Trans. Amer. Math. Soc. 283 (1984), no. 2, 383–421. MR 737876, DOI 10.1090/S0002-9947-1984-0737876-X
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 1299-1304
- MSC: Primary 55P42; Secondary 55P35
- DOI: https://doi.org/10.1090/S0002-9939-1988-0955026-0
- MathSciNet review: 955026