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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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


Author: Warren M. Krueger
Journal: Trans. Amer. Math. Soc. 228 (1977), 85-97
MSC: Primary 55H15; Secondary 57D90
MathSciNet review: 0431171
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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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DOI: https://doi.org/10.1090/S0002-9947-1977-0431171-0
Keywords: Adams spectral sequence, framed manifold, Wu class, Kervaire invariant
Article copyright: © Copyright 1977 American Mathematical Society