Topology Seminar: Combinatorial models for stable homotopy theory

We will recall the definition of dendroidal sets as a generalization of simplicial sets, and present the connection (Quillen equivalence) to connective spectra which gives a factorization of the so-called K-theory spectrum functor from symmetric monoidal categories to spectra. We will present a common generalization of  two results of Thomason: 1) posets model all homotopy types; 2) symmetric monoidal categories model all connective spectra. We will introduce a notion of multiposets (special type of coloured operads) and of the subdivision of dendroidal sets which can be used to show that multiposets model all connective spectra. If time permits we will mention homology of dendroidal sets as it provides a means to define equivalences of multiposets in an internal combinatorial way.