Title of Paper: The weak conjecture on spherical classes

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: Let $A$ be the mod 2 Steenrod algebra. We construct a
chain-level representation of the dual of Singer's algebraic
transfer,
$$
Tr_k^*: Tor^A_k(F_2,F_2) \to F_2\otimes_A F_2[x_1,...,x_k],
$$
which maps Singer's invariant-theoretic model of the lambda
algebra to $F_2[x_1^{\pm},...,x_k^{\pm}]$ and is the inclusion of
the Dickson algebra into the polynomial algebra
$F_2[x_1,...,x_k]$.

Based on this chain-level representation, we study some aspects of
the weak conjecture on spherical classes and prove it in some
special cases.

(Address of Paper: Math. Zeit. 231 (1999), 727-743)