Journal of the Mathematical Society of Japan

On framed simple Lie groups

Haruo MINAMI

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Abstract

For a compact simple Lie group $G$, we show that the element $[G, \mathcal{L}] \in \pi^S_*(S^0)$ represented by the pair $(G, \mathcal{L})$ is zero, where $\mathcal{L}$ denotes the left invariant framing of $G$. The proof relies on the method of E. Ossa [Topology, 21 (1982), 315–323].

Article information

Source
J. Math. Soc. Japan, Volume 68, Number 3 (2016), 1219-1229.

Dates
First available in Project Euclid: 19 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1468956166

Digital Object Identifier
doi:10.2969/jmsj/06831219

Mathematical Reviews number (MathSciNet)
MR3523545

Zentralblatt MATH identifier
1351.57029

Subjects
Primary: 57R15: Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
Secondary: 22E46: Semisimple Lie groups and their representations 19L20: $J$-homomorphism, Adams operations [See also 55Q50]

Keywords
framed manifolds Lie groups Adams conjecture

Citation

MINAMI, Haruo. On framed simple Lie groups. J. Math. Soc. Japan 68 (2016), no. 3, 1219--1229. doi:10.2969/jmsj/06831219. https://projecteuclid.org/euclid.jmsj/1468956166


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