19 February 2014
The classical small cancellation theory goes back to the 1950's and 1960's when the geometry of 2-complexes with a unique 0-cell was studied, i.e. the standard 2-complex of a finite presentation. D.T. Wise generalizes the Small Cancellation Theory to 2-complexes with arbitray 0-cells showing that certain classes of Small Cancellation Groups act properly discontinuously and cocompactly on CAT(0) Cube complexes and hence have codimesion 1-subgroups. To be more precise I will introduce "his" version of small Cancellation Theory and go roughly through the main ideas of his construction of the cube complex using Sageeve's famous construction. I'll try to make the ideas intuitively clear by using many pictures. The goal is to show that B(4)-T(4) and B(6)-C(7) groups act properly discontinuously and cocompactly on CAT(0) Cube complexes and if there is time to explain the difficulty of the B(6) case. The talk should be self contained. So don't worry if you have never had heard about "Small Cancellation".