Algebra/Topology Seminar

Jérôme Scherer (EPFL): Cellularity and nilpotency

This is joint work with W. Chacholski, E. Dror Farjoun, and R. Flores. Usually one considers Eilenberg-MacLane spaces and Postnikov sections as basic building blocs to construct arbitrary spaces. We turn everything upside down and show that it is possible to construct the Postnikov sections of a (nilpotent) space with this space. Ingredients such as a cellular version of the Blakers-Massey theorem (work with K. Werndli), or a study of discrete spaces of pointed self-maps, are used. Applications will be presented: to cellularization of classifying spaces of discrete groups for example, and to acyclicity of Postnikov sections.