School of Mathematics & Physics, University of Lincoln
On the 17th of September 2019 Rudradip Biswas (University of Manchester) visited Charlotte Scott Centre for Algebra and gave a talk “Towards an Algebraic Characterisation of Kropholler’s Hierarchy through Some Generation Results”.
Abstract: I will start by defining a notion of generation for modules that can be said to have been inspired from some notions of generation for triangulated categories which have been looked into by Rouquier, Rickard, and others. I will then prove a number of useful general results regarding generation of modules using my definition of generation, look into the significance of a module being generated in a finite number of steps by a class (in my definition) and investigate when that is equivalent to the same module admitting finite resolutions by modules of that class. I will also show how this notion of generation can be used to provide examples of classes that admit certain interesting properties regarding modules generated by them, and, finally, establish some new properties of modules of groups that lie in Kropholler’s hierarchy. I will end by explaining how these new properties of modules of groups in Kropholler’s hierarchy can be used to formulate an entirely algebraic hierarchy of groups similar to Kropholler’s hierarchy which is geometric in nature.