During my first year I have been working on cutting and pasting of manifolds. This idea grew out of a series of papers by Jaenich which studied the Novikov additivity of the signature. The cut and paste operation gives rise to different types of groups: the (Schneiden und Kleben) SK-groups, the bordism SK-groups and furthermore the SKK groups. The theory about these groups and their relation with cobordism theory was developed in Cutting and Pasting of Manifolds; SK-Groups by U.Karras, M.Kreck, W.D Neumann and E.Ossa.

The first chapter in my First year report "algebraic and geometric cutting and pasting of manifolds" reviews the main ideas about SK-groups, while the second chapter investigates an algebraic interpretation of these ideas. For a brief review of this algebraic interpretation see "Cutting and Pasting manifolds from the algebraic point of view" by A. Ranicki The report does not include the definition of the SKK-groups, which have become relevant in the application to TQFT developed recently by Matthias Kreck. Here is a note on SKK groups, that I wrote during the first term.

On Monday 1st october Matthias kreck gave a talk for the Topology seminar on TQFT and SKK groups.There is a video of this lecture available on request (email me if you would like to view this video). Here are my notes for this talk. -