Title of Paper: Spherical classes and the algebraic transfer

Author: Nguy\^{e}n H. V. Hung

1991 Mathematics Subject Classification: Primary 55P47, 55Q45,
55S10, 55T15.

Address of Author: Department of Mathematics, Vietnam National
University, Hanoi, 334 Nguyen Trai Street, Hanoi, Vietnam

E-mail address: nhvhung@vnu.edu.vn


Abstract: We study a weak form of the classical conjecture which
predicts that there are no spherical classes in $Q_0S^0$ except
the elements of Hopf invariant one and those of Kervaire invariant
one. The weak conjecture is obtained by restricting the Hurewicz
homomorphism to the homotopy classes which are detected by the
algebraic transfer.

We prove that the weak conjecture is equivalent to the following
one: Every positive degree Dickson invariant of at least 3
variables  belongs to the image of the Steenrod algebra acting on
the corresponding polynomial algebra. This conjecture is proved
for the case of 3 variables in two different ways.