
Mathematics 2007
Operations on Atheoretic niltermsAbstract: For a space X, we define Frobenius and Verschiebung operations on the nilterms NA^{fd} (X) in the algebraic Ktheory of spaces, in three different ways. Two applications are included. Firstly, we obtain that the homotopy groups of NA^{fd} (X) are either trivial or not finitely generated as abelian groups. Secondly, the Verschiebung defines a Z[N_x]module structure on the homotopy groups of NA^{fd} (X), with N_x the multiplicative monoid. We also we give a calculation of the homotopy groups of the nilterms NA^{fd} (*) after pcompletion for an odd prime p as Z_p[N_x]modules up to dimension 4p7. We obtain nontrivial groups only in dimension 2p2, where it is finitely generated as a Z_p[N_x]module, and in dimension 2p1, where it is not finitely generated as a Z_p[N_x]module.
