Semra Pamuk

• Middle East Technical University

Let M be a closed, connected, orientable topological $4$ -manifold, and G be a finite group acting topologically and locally linearly on M . In this paper, we investigate the spectral sequence for the Borel cohomology $H^*_G(M)$ and establish new bounds on the rank of G for homologically trivial actions with discrete singular set.

Let M be a closed, connected, orientable topological 4-manifold, and G be a finite group acting topologically and locally linearly on M. In this paper we investigate the Borel spectral sequence for the G-equivariant cohomology of M, and establish new bounds on the rank of G for homologically trivial actions with discrete singular set.

Let $G$ be a finite group and $\cF$ be a family of subgroups of $G$ closed under conjugation and taking subgroups. We consider the question whether there exists a periodic relative $\cF$-projective resolution for $\bbZ$ when $\cF$ is the family of all subgroups $H \leq G$ with $\rk H \leq \rk G-1$. We answer this question negatively by calculating...

The aim of this paper is to present a general method to construct projective resolutions of globally defined Mackey functors over a field of characteristic zero and apply it to obtain explicit resolutions for inflation functors. Our method is a special case of Bouc’s method in (Proc. Symp. Pure Math. 63 (1998), 31–84) and uses global Mackey functor...

We give a general framework for studying G-CW complexes via the orbit category. As an application we show that the symmetric group G=S_5 admits a finite G-CW complex X homotopy equivalent to a sphere, with cyclic isotropy subgroups. Comment: 48 pages. The results are unchanged, but revisions to the exposition have been made following a referee's re...

In this thesis, non-free actions of a finite group with a given family of isotropy subgroups are considered. An algebraic setting is established to study these actions. It is proved that if a finite group has periodic cohomology of period n with respect to a given family, then there exists a periodic relative projective resolution of length n. The...

Thesis for the degree of Master of Science in the Department of Mathematics.