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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

$ v\sb 1$-periodic homotopy groups of exceptional Lie groups: torsion-free cases


Authors: Martin Bendersky, Donald M. Davis and Mamoru Mimura
Journal: Trans. Amer. Math. Soc. 333 (1992), 115-135
MSC: Primary 57T20
MathSciNet review: 1116310
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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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DOI: https://doi.org/10.1090/S0002-9947-1992-1116310-9
Keywords: Exceptional Lie groups, periodic homotopy groups, unstable Novikov spectral sequence
Article copyright: © Copyright 1992 American Mathematical Society