24/04/2007, 16:30 — 17:30 — Room P3.10, Mathematics Building Emmanuel Dror-Farjoun, Hebrew University of Jerusalem
Cellularization in Algebra and Topology
The talk will outline basic constructions and properties of cellular approximation, mostly in homological algebra and group theory. Cellular approximation attempts to examine spaces or groups by constructing "approximations" using a chosen group or space such as a sphere, a given finite group, or a given chain complex. Examples are taking the subgroup generated by torsion elements, taking the canonical central extension or taking the usual CW-approximation for spaces. It turns out that very general constructions can be presented as cellular approximations. One gets a functor which has interesting properties: For example they alway turn a finite group into a finite group and the same for nilpotent groups and spaces. Sometimes this can help the study of more complicated spaces and chain complexes. An example, is the (K-theoretical) chain complex of a fiber of a given map, or the chain complex of the homotopy fixed points of a group action on a space.
