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Hurewicz images in BP and the Arf-Kervaire invariant

Published online by Cambridge University Press:  18 July 2002

Victor P. Snaith
Victor P. Snaith
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton SO17 1BJ, England e-mail: vps@maths.soton.ac.uk
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In this paper BP-theory is used to give a proof that there exists a stable homotopy element in \pi _{2^{n+1} - 2}^{S}( {\tf="times-b"R}P^{\infty }) with non-zero Hurewicz image in ju-theory if and only if there exists an element of \pi _{2^{n+1} - 2}^{S}( S{\hskip1}^{0}) that is represented by a framed manifold of Arf invariant one.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 1 , January 2002 , pp. 9 - 27
Copyright
2002 Glasgow Mathematical Journal Trust