Supervisors info:
Εµµανουήλ Ιωάννης (επιβλ.) - Καθηγητής , Τμήμα Μαθηματικών
Βάρσος ∆ηµήτριος - Καθηγητής , Τμήμα Μαθηματικών
Ντόκας Ιωάννης - Επίκουρος Καθηγητής , Τμήμα Μαθηματικών
Summary:
Homology and Cohomology are generally considered as duals of each other. But for a finite group G their properties seem more “similar” than dual. Tate cohomology is a good way to describe those similarities. After the description of the corresponding theory, we will proceed to the presentation of equivariant homology which equips with a tool for drawing conclusions regarding G from G’s action on X, where X is a topological space. The definition of H∗(G, M) and H∗(G, M) allows for the choice of arbitrary projective resolutions i.e. P = (Pi)i≥0 of Z
over ZG. Similarly, from the topology point of view, we can calculate H∗(G, M) and H∗(G, M) via an arbitrary K(G, 1)-complex Y . Since there is this freedom of choice, it is natural to try and choose P (of Y ) as “small” as possible. This will lead us to various finiteness conditions in G. In the process we will encounter and analyse numerous key theorems which have various aspects and are interesting by their own.
