Three contributions to the homotopy theory of the exceptional Lie groups G2 and F*4

Donald M. DAVIS; Mark MAHOWALD

doi:10.2969/jmsj/04340661

Three contributions to the homotopy theory of the exceptional Lie groups G₂ and F^*₄

Donald M. DAVIS, Mark MAHOWALD

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1991 年 43 巻 4 号 p. 661-671

DOI https://doi.org/10.2969/jmsj/04340661

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Published: 1991 Received: 1990/05/18 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文タイトル訂正内容: Wrong : Three contributions to the homotopy theory of the exceptional Lie groups G₂ and F*₄
Right : Three contributions to the homotopy theory of the exceptional Lie groups G₂ and F^*₄

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) J. F. Adams, On the groups J(X)-IV, Topology, 5 (1966), 21-71.
2) M. F. Atiyah, Thom complexes, Proc. London Math. Soc., 11 (1961), 291-310.
3) W. D. Barcus and J.-P. Meyer, The suspension of a loop space, Amer. Jour. Math., 80 (1958), 895-920.
4) D. Barnes, D. Poduska and P. Shick, Unstable Adams spectral sequence charts, to appear in Amer. Jour. Math..
5) M. Bendersky and D. M. Davis, 2-primary v₁-periodic homotopy groups of SU(n), to appear.
6) A. Borel, Sur l'homologie et la cohomology des groupes de Lie compacts connexes, Amer. Jour. Math., 76 (1954), 273-342.
7) A. Borel, Le plan projectif des octaves et les spheres comme espaces homogènes, Comptes rendus de l'Académie des Sciences, 230 (1950), 1378-1380.
8) A. K. Bousfield, The localization of spectra with respect to homology, Topology, 18 (1979), 257-281.
9) A. K. Bousfield, K-localizations and K-equivalences of infinite loop spaces, Proc. London Math. Soc., 44 (1982), 291-311.
10) F. R. Cohen, J. C. Moore and J. A. Neisendorfer, The double suspension and exponents of the homotopy groups of spheres, Ann. of Math., 110 (1979), 549-565.
11) D. M. Davis, v₁-periodic homotopy groups of SU(n) at an odd prime, to appear in Jour. London Math. Soc..
12) D. M. Davis and M. Mahowald, v₁-periodic homotopy groups of Sp(2), Sp(3), and S²ⁿ, Proc, of 1988 Conference in Kinosaki, Springer-Verlag, Lecture Notes in Math., 1418 (1990), 219-237.
13) D. M. Davis and M. Mahowald, v₁-periodicity in the unstable Adams spectral sequence, Math. Z., 204 (1990), 319-339.
14) D. M. Davis and M. Mahowald, Homotopy groups of some mapping telescopes, Annals of Math. Stud., 113 (1987), 126-151.
15) E. Halpern, The cohomology algebra of certain loop spaces, Proc. Amer. Math. Soc., 9(1958), 808-817.
16) I. M. James, Reduced product spaces, Annals of Math., 62 (1955), 170-197.
17) M. Mahowald, The image of J in the EHP sequence, Ann, of Math., 116 (1982), 65-112.
18) M. Mahowald and R. D. Thompson, Unstable compositions related to the image of J, Proc. Amer. Math. Soc., 102 (1988), 431-436.
19) M. Mahowald and R. D. Thompson, The K-theory localization of an unstable sphere, to appear in Topology.
20) M. Mimura, The homotopy groups of Lie groups of low rank, Jour. Math. Kyoto Univ., 6(1967), 131-176.
21) M. Mimura and H. Toda, Cohomology operations and the homotopy of compact Lie groups, Topology, 9(1970), 317-336.
22) M. Mimura and H. Toda, Homotopy groups of SU(3), SU(4), and Sp(2), Jour. Math. Kyoto Univ., 3(1964), 217-250.
23) N. Oda, Periodic families in the homotopy groups of SU(3), SU(4), Sp(2), and G₂, Mem. Fac. Sci. Kyushu Univ., 32 (1978), 277-290.
24) P. Selick, 2-primary exponents for the homotopy groups of spheres, Topology, 23 (1984), 97-99.
25) V.P. Snaith, A stable decomposition for ΩⁿSⁿX, Jour. London. Math. Soc., 7 (1974), 577-583.

Right : [1] J. F. Adams, On the groups J(X)-IV, Topology, 5 (1966), 21-71.
[2] M. F. Atiyah, Thom complexes, Proc. London Math. Soc., 11 (1961), 291-310.
[3] W. D. Barcus and J. -P. Meyer, The suspension of a loop space, Amer. Jour. Math., 80 (1958), 895-920.
[4] D. Barnes, D. Poduska and P. Shick, Unstable Adams spectral sequence charts, to appear in Amer. Jour. Math..
[5] M. Bendersky and D. M. Davis, 2-primary v₁-periodic homotopy groups of SU(n), to appear.
[6] A. Borel, Sur l'homologie et la cohomology des groupes de Lie compacts connexes, Amer. Jour. Math., 76 (1954), 273-342.
[7] A. Borel, Le plan projectif des octaves et les sphères comme espaces homogènes, Comptes rendus de l'Académie des Sciences, 230 (1950), 1378-1380.
[8] A. K. Bousfield, The localization of spectra with respect to homology, Topology, 18 (1979), 257-281.
[9] A. K. Bousfield, K-localizations and K-equivalences of infinite loop spaces, Proc. London Math. Soc., 44 (1982), 291-311.
[10] F. R. Cohen, J. C. Moore and J. A. Neisendorfer, The double suspension and exponents of the homotopy groups of spheres, Ann. of Math., 110 (1979), 549-565.
[11] D. M. Davis, v₁-periodic homotopy groups of SU(n) at an odd prime, to appear in Jour. London Math. Soc..
[12] D. M. Davis and M. Mahowald, v₁-periodic homotopy groups of Sp(2), Sp(3), and S²ⁿ, Proc. of 1988 Conference in Kinosaki, Springer-Verlag, Lecture Notes in Math., 1418 (1990), 219-237.
[13] D. M. Davis and M. Mahowald, v₁-periodicity in the unstable Adams spectral sequence, Math. Z., 204 (1990), 319-339.
[14] D. M. Davis and M. Mahowald, Homotopy groups of some mapping telescopes, Annals of Math. Stud., 113 (1987), 126-151.
[15] E. Halpern, The cohomology algebra of certain loop spaces, Proc. Amer. Math. Soc., 9 (1958), 808-817.
[16] I. M. James, Reduced product spaces, Annals of Math., 62 (1955), 170-197.
[17] M. Mahowald, The image of J in the EHP sequence, Ann. of Math., 116 (1982), 65-112.
[18] M. Mahowald and R. D. Thompson, Unstable compositions related to the image of J, Proc. Amer. Math. Soc., 102 (1988), 431-436.
[19] M. Mahowald and R. D. Thompson, The K-theory localization of an unstable sphere, to appear in Topology.
[20] M. Mimura, The homotopy groups of Lie groups of low rank, Jour. Math. Kyoto Univ., 6 (1967), 131-176.
[21] M. Mimura and H. Toda, Cohomology operations and the homotopy of compact Lie groups, Topology, 9 (1970), 317-336.
[22] M. Mimura and H. Toda, Homotopy groups of SU(3), SU(4), and Sp(2), Jour. Math. Kyoto Univ., 3 (1964), 217-250.
[23] N. Oda, Periodic families in the homotopy groups of SU(3), SU(4), Sp(2), and G₂, Mem. Fac. Sci. Kyushu Univ., 32 (1978), 277-290.
[24] P. Selick, 2-primary exponents for the homotopy groups of spheres, Topology, 23 (1984), 97-99.
[25] V. P. Snaith, A stable decomposition for ΩⁿSⁿX, Jour. London. Math. Soc., 7 (1974), 577-583.

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