v 1 -Periodic Homotopy Groups of Exceptional Lie Groups: Torsion-Free Cases

1992 ◽  
Vol 333 (1) ◽  
pp. 115 ◽  
Author(s):  
Martin Bendersky ◽  
Donald M. Davis ◽  
Mamoru Mimura
Keyword(s):  
Lie Groups ◽  
Homotopy Groups ◽  
Exceptional Lie Groups ◽  
Torsion Free

scholarly journals NOTE ON SAMELSON PRODUCTS IN EXCEPTIONAL LIE GROUPS

2020 ◽  
pp. 1-12
Author(s):  
DAISUKE KISHIMOTO ◽  
AKIHIRO OHSITA ◽  
MASAHIRO TAKEDA
Keyword(s):  
Lie Groups ◽  
Exceptional Lie Groups ◽  
Torsion Free

Abstract We determine the (non-)triviality of Samelson products of inclusions of factors of the mod p decomposition of $G_{(p)}$ for $(G,p)=(E_7,5),(E_7,7),(E_8,7)$ . This completes the determination of the (non-)triviality of those Samelson products in p-localized exceptional Lie groups when G has p-torsion-free homology.

scholarly journals Samelson products in p-regular exceptional Lie groups

2014 ◽  
Vol 178 ◽  
pp. 17-29 ◽  
Author(s):  
Sho Hasui ◽  
Daisuke Kishimoto ◽  
Akihiro Ohsita
Keyword(s):  
Lie Groups ◽  
Exceptional Lie Groups

scholarly journals The Exponent of the Homotopy Groups of Moore Spectra and the Stable Hurewicz Homomorphism

1996 ◽  
Vol 48 (3) ◽  
pp. 483-495 ◽  
Author(s):  
Dominique Arlettaz
Keyword(s):  
Abelian Group ◽  
Positive Integer ◽  
Upper Bound ◽  
Homology Theory ◽  
Homotopy Groups ◽  
Integral Homology ◽  
Ring Spectrum ◽  
Bounded Below ◽  
Torsion Free ◽  
Ordinary Integral

AbstractThis paper shows that for the Moore spectrum MG associated with any abelian group G, and for any positive integer n, the order of the Postnikov k-invariant kn+1(MG) is equal to the exponent of the homotopy group πnMG. In the case of the sphere spectrum S, this implies that the exponents of the homotopy groups of S provide a universal estimate for the exponent of the kernel of the stable Hurewicz homomorphism hn: πnX → En(X) for the homology theory E*(—) corresponding to any connective ring spectrum E such that π0E is torsion-free and for any bounded below spectrum X. Moreover, an upper bound for the exponent of the cokernel of the generalized Hurewicz homomorphism hn: En(X) → Hn(X; π0E), induced by the 0-th Postnikov section of E, is obtained for any connective spectrum E. An application of these results enables us to approximate in a universal way both kernel and cokernel of the unstable Hurewicz homomorphism between the algebraic K-theory of any ring and the ordinary integral homology of its linear group.

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