𝑣₁-periodic homotopy groups of exceptional Lie groups: torsion-free cases

Bendersky, Martin; Davis, Donald M.; Mimura, Mamoru

doi:10.1090/S0002-9947-1992-1116310-9

$v_ 1$-periodic homotopy groups of exceptional Lie groups: torsion-free cases
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by Martin Bendersky, Donald M. Davis and Mamoru Mimura

Trans. Amer. Math. Soc. 333 (1992), 115-135

DOI: https://doi.org/10.1090/S0002-9947-1992-1116310-9

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Abstract:

The ${v_1}$-periodic homotopy groups $v_1^{ - 1}{\pi _ {\ast } }(X;p)$ are computed explicitly for all pairs $(X,p)$, where $X$ is an exceptional Lie group whose integral homology has no $p$-torsion. This yields new lower bounds for $p$-exponents of actual homotopy groups of these spaces. Delicate calculations with the unstable Novikov spectral sequence are required in the proof.

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