References
[B-L-M&] Bruner, R., Lewis, G., May, J.P., McClure, J., Steinberger, M.:H ∞ ring spectra and their applications. (Lect. Notes Math., vol. 1176) Berlin Heidelberg New York: Springer 1988
[B-M] Barcus, W.D., Meyer, J.P.: The suspension of a loop space. Am. J. Math.80, 895–920 (1958)
[B-S] Boardman, J.M., Steer, B.: On Hopf invariants. Comment. Math. Helv.42, 217–224 (1968)
[Ba1] Barratt, M.G.: Higher Hopf invariants. Mimeographed notes, University of Chicago 1957
[Ba2] Barratt, M.G.: The spectral sequence of an inclusion, pp. 22–27. Aarhus: Colloq. algebr. Topology 1962
[C-H-P] Cohen, F., Hopkins, M., Peterson, F.: ΩSU (3) splits in a finite number of suspensions. Unpublished, 1985
[C-M] Crabb, M.C., Mitchell, S.A.: The loops onU(n)/O(n) andU(2n)/Sp(n). Math. Proc. Camb. Philos. Soc.104, 95–103 (1988)
[C-M-T] Cohen, F.R., May, J.P., Taylor, L.R.:K (ℤ, 0), andK (ℤ/2, 0) as Thom spectra. Ill. J. Math25, 99–106 (1981)
[D-M] Davis, D., Mahowald, M.: In: Kane, R.M. et al. (eds.) Current trends in algebraic topology. Ext over the subalgebraA 2 of the Steenrod algebra for stunted projective spaces. (C.M.S. Conf. Proc., vol. 2, part 1, pp. 297–342) Providence, RI: Am. Math. Soc. 1982
[Ga1] Ganea, T.: A generalization of the homology and homotopy suspension. Comment. Math. Helv.39, 295–322 (1964)
[Ga2] Ganea, T.: Induced fibrations and cofibrations. Trans. Am. Math. Soc.127, 442–459 (1967)
[Ga3] Ganea, T.: Monomorphisms and relative Whitehead products. Topology10, 391–403 (1971)
[Ga4] Ganea, T.: On the homotopy suspension. Comment. Math. Helv.43, 225–234 (1968)
[Gr1] Gray, B.: On the homotopy groups of mapping cones. Proc. Lond. Math. Soc.26, 497–520 (1973)
[Gr2] Gray, B.: On Toda's fibration. Proc. Lond. Math. Soc.97, 289–298 (1985)
[Hi] Hilton, P.: A remark on loop spaces. Proc. Am. Math. Soc.15, 596–600 (1964)
[Ho] Hopkins, M.: Stable decompositions of certain loop spaces. Ph.D. thesis, Northwestern University 1984
[M-N] Moore, J., Neisendorfer, J.: Equivalence of Toda-Hopf invariants. Isr. J. Math.66, 300–318 (1989)
[M-P] Mahowald, M., Peterson, F.: Secondary operations on the Thom class. Topology2, 367–377 (1964)
[Ma1] Mahowald, M.: The index of a tangent 2-field. Pac. J. Math.58, 539–548 (1975)
[Ma2] Mahowald, M.: Thom spectra which are ring spectra. Duke J.46, 549–559 (1979)
[Mi1] Milgram, J.: The bar construction and abelianH-spaces. Ill. J. Math.11, 242–250 (1967)
[Mi2] Mitchell, S.A.: A filtration of the loops on SU(n) by Schubert varieties. Math. Z.193, 347–362 (1986)
[Pr] Pressley A.: Decompositions of the space of loops on a Lie group. Topology19, 65–79 (1980)
[Ri1] Richter, W.: A partial Cartan formula for the stable splitting of ΩU(n), and a stable splitting of the loops on a infinite complex Stiefel manifold. Trans. Am. Math. Soc. (in press)
[Ri2] Richter, W.: Towards Poincaré surgery I: A homotopy theoretic proof of Williams's Poincaré embedding theorem. (Preprint 1988)
[Se] Segal, G.B.: Notes on harmonic maps (after K. Uhlenbeck). In: Sutherland, W., et al. (eds.) Conference in honor of I.M. James. (Lond. Math. Soc. Lect. Note Ser., vol. 139, pp. 153–164) Cambridge: Cambridge University Press 1990
[Sn] Snaith, V.P.: Algebraic cobordism andK-theory. Mem. Am. Math. Soc.221 (1979)
[St] Stassheff, J.:H-spaces from a homotopy point of view. (Lect. Notes Math., vol. 161) Berlin Heidelberg New York: Springer 1970
[To1] Toda, H.: Composition Methods in the Homotopy Groups of Spheres. Princeton: Princeton University Press 1962
[To2] Toda, H.: On the double suspensionE 2. J. Inst. Polytechnics, Osaka City Univ., Ser. A7, 103–145 (1956)
[Wh1] Whitehead, G.W.: Elements of Homotopy Theory. (Grad. Texts Math., vol. 61) Berlin Heidelberg New York: Springer 1978
[Wh2] Whitehead, G.W.: On the homology suspension. Ann. Math.2, 254–268 (1955)
[Wi] Williams, B.: Hopf invariants, localizations, and embeddings of Poincaré complexes. Pac. J. Math.84, 217–224 (1979)
Author information
Authors and Affiliations
Additional information
Supported by a grant from the NSF
Rights and permissions
About this article
Cite this article
Mahowald, M., Richter, W. ΩSU (3) splits after four suspensions, but not two. Math Z 208, 597–615 (1991). https://doi.org/10.1007/BF02571548
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02571548