Hurewicz images in BP and the Arf-Kervaire invariant
Glasgow mathematical journal, Tome 44 (2002) no. 1, pp. 9-27

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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.
Snaith, Victor P. Hurewicz images in BP and the Arf-Kervaire invariant. Glasgow mathematical journal, Tome 44 (2002) no. 1, pp. 9-27. doi: 10.1017/S0017089502010017
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