Cycles and Spectra

Some recent work on spaces of algebraic cycles is surveyed. The main focus is on spaces of real and quaternionic cycles and their relation to equivariant Eilenberg- MacLane spaces.Dedicated to IMPA on the occasion of its 50^th anniversary     

Endomorphisms of H *(K(V, n); ) in the category of unstable modules

The ring of endomorphisms of the -cohomology of the Eilenberg-MacLane space K(V,n), in the category of unstable modules over the Steenrod algebra is calculated, where V is an elementary abelian 2-group, n is a non-negative integer and is the prime field of characteristic two. The result generalizes the theorem of Adams, Gunawardena and Miller, which corresponds to the case n=1.     

Rational Mackey functors for compact lie groups I

A Mackey functor M is a structure analogous to the representationring functor H R(H) encoding good formal behaviour under inductionand restriction. More explicitly, M associates an abelian groupM(H) to each closed subgroup H of a fixed compact Lie groupG, and to each inclusion K H it associates a restriction map and an induction map . This paper gives an analysis of thecategory of Mackey functors M whose values are rational vectorspaces: such a Mackey functor may be specified by giving a suitablycontinuous family consisting of a Q ₀(W_G(H))-module V(H) foreach closed subgroup H with restriction maps V(K) V(K) wheneverK is normal in K and K/K is a torus (a ‘continuous Weyl-toralmodule’). We show that the category of rational Mackeyfunctors is equivalent to the category of rational continuousWeyl-toral modules. In Part II this will be used to give analgebraic analysis of the category of rational Mackey functors,showing in particular that it has homological dimension equalto the rank of the group. 1991 Mathematics Subject Classification:19A22, 20C99, 22E15, 55N91, 55P42, 55P91.     

Nullification and cellularization of classifying spaces of finite groups

In this note we discuss the effect of the -nullification and the -cellularization over classifying spaces of finite groups, and we relate them with the corresponding functors with respect to Moore spaces that have been intensively studied in the last years. We describe by means of a covering fibration, and we classify all finite groups for which is -cellular. We also carefully study the analogous functors in the category of groups, and their relationship with the fundamental groups of and