Hopf invariants and Browder’s work on the Kervaire invariant problem

Krueger, Warren M.

doi:10.1090/S0002-9947-1977-0431171-0

Hopf invariants and Browder’s work on the Kervaire invariant problem
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by Warren M. Krueger

Trans. Amer. Math. Soc. 228 (1977), 85-97

DOI: https://doi.org/10.1090/S0002-9947-1977-0431171-0

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Abstract:

In this paper we calculate certain functional differentials in the Adams spectral sequence converging to Wu cobordism whose values may be thought of as Hopf invariants. These results are applied to reobtain Browder’s characterization: if $q + 1 = {2^k}$, there is a 2q dimensional manifold of Kervaire invariant one if and only if $h_k^2$ survives to ${E_\infty }({S^0})$.

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