Özgün Ünlü

Semigroup Actions on Sets and the Burnside Ring

In this paper we discuss some enlargements of the category of sets with semigroup actions and equivariant functions. We show that these enlarged categories possess two idempotent endofunctors. In the case of groups these enlarged categories are equivalent to the usual category of group actions and equivariant functions, and these idempotent endofunctors reverse a given action. For a general semigroup we show that these enlarged categories admit homotopical category structures defined by using these endofunctors and show that up to homotopy these categories are equivalent to the usual category of sets with semigroup actions. We finally construct the Burnside ring of a monoid by using homotopical structure of these categories, so that when the monoid is a group this definition agrees with the usual definition, and we show that when the monoid is commutative, its Burnside ring is equivalent to the Burnside ring of its Gröthendieck group.

Fusion systems and group actions with abelian isotropy subgroups

We prove that if a finite group

Free actions of finite groups on S^n x S^n

G

Gröbnerian Dickson polynomials

acts smoothly on a manifold

On Ranks for Finite Supersolvable Groups and Actions on Products of Spheres

M

Fixity and free group actions on products of spheres

so that all the isotropy subgroups are abelian groups with rank

Fusion systems and constructing free actions on products of spheres

\leq k

Constructing homologically trivial actions on products of spheres

, then

EXAMPLES OF FREE ACTIONS ON PRODUCTS OF SPHERES

G

Quasilinear actions on products of spheres

acts freely and smoothly on