3-primary v1-periodic homotopy groups of E7
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Abstract
We compute the 3-primary v1-periodic homotopy groups of the exceptional Lie group E7. Now E8 at the primes 3 and 5 is the only compact simple Lie group whose odd-primary v1-periodic homotopy groups remian to be computed. The main work is computing the unstable Novikov spectral sequence of \Omega E7/Sp(2). Showing that this converges to v1-periodic homotopy groups requires recent work of Bousfield and Bendersky-Thompson.Keywords
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This publication has 11 references indexed in Scilit:
- The Bousfield-Kan spectral sequence for periodic homology theoriesAmerican Journal of Mathematics, 2000
- The mod 3 homology of the space of loops on the exceptional Lie groups and the adjoint actionKyoto Journal of Mathematics, 1997
- Tractable formulas for v 1periodic homotopy groups of SU (n)when n≤p 2 -p + 1Forum Mathematicum, 1996
- v1-periodic homotopy groups ofSp(n)Pacific Journal of Mathematics, 1995
- The ν 1 -Periodic Homotopy Groups of SU(n ) at Odd PrimesJournal of the London Mathematical Society, 1991
- The Double Suspension and Exponents of the Homotopy Groups of SpheresAnnals of Mathematics, 1979
- The unstable Adams spectral sequence for generalized homologyTopology, 1978
- The Hopf ring for complex cobordismJournal of Pure and Applied Algebra, 1977
- Cohomology Operations and the Hopf Algebra Structures of the Compact, Exceptional Lie Groups E 7 and E 8Proceedings of the London Mathematical Society, 1977
- On the K-Theory of Homogeneous Spaces and Conjugate Bundles of Lie GroupsProceedings of the London Mathematical Society, 1971