Some aspects of equivariant LS-category

Equivariant LS-category for finite group actions

In this paper we study the equivariant category of finite group actions. We introduce the basic filtration for the orbit space of the action. In terms of this filtration we give upper and lower estimates of the equivariant category. The idea for the proof is parallel to the approach in [3] for compact-Hausdorff foliations. We give examples to show that both the upper and lower bounds are realiz...

Categorical aspects of equivariant homotopy

Equivariant Cw-complexes and the Orbit Category

We give a general framework for studying G-CW complexes via the orbit category. As an application we show that the symmetric group G = S5 admits a finite G-CW complex X homotopy equivalent to a sphere, with cyclic isotropy subgroups.

The Bounded below Equivariant Derived Category

In this note, we give show how the equivariant derived category of Bernstein and Lunts can be extended to a purely algebraic setting, without the use of the theory of stacks. In particular, we show that it is possible to use the yoga of weights in the equivariant derived category, as one would in the usual derived category of a scheme over a finite field.

Equivariant derived category and representation of real semisimple Lie groups