Ergun Yalcin

Group actions and group extensions

In this paper we study finite group extensions represented by special cohomology classes. As an application we obtain some restrictions on finite groups which can act freely on a product of spheres or on a product of real projective spaces. In particular, we prove that if (Z/p) acts freely on (S), then r ≤ k.

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 nite G-CW complex X homotopy equivalent to a sphere, with cyclic isotropy subgroups.

On nilpotent ideals in the cohomology ring of a finite group

In this paper we find upper bounds for the nilpotency degree of some ideals in the cohomology ring of a finite group by studying fixed point free actions of the group on suitable spaces. The ideals we study are the kernels of restriction maps to certain collections of proper subgroups. We recover the Quillen-Venkov lemma and the Quillen F-injectivity theorem as corollaries, and discuss some generalizations and further applications. We then consider the essential cohomology conjecture, and show that it is related to group actions on connected graphs. We discuss an obstruction to constructing a fixed point free action of a group on a connected graph with zero “k-invariant” and study the class related to this obstruction. It turns out that this class is a “universal essential class” for the group and controls many questions about the groups essential cohomology and tranfers from proper subgroups. 2000 Mathematics Subject Classification. Primary: 20J06; Secondary: 57S17.

Fusion systems and group actions with abelian isotropy subgroups

We prove that if a finite group

Free actions on products of spheres at high dimensions

G

A note on Serre’s theorem in group cohomology

acts smoothly on a manifold

Free actions of p-groups on products of lens spaces

M

Representation rings for fusion systems and dimension functions

so that all the isotropy subgroups are abelian groups with rank

Relative Group Cohomology and The Orbit Category

\leq k

An induction theorem for the unit groups of Burnside rings of 2-groups

, then