Processing math: 100%
homeHome ViewLayout PrintPrinter Friendly   searchSearch LoginAdd Event
Mathematics Calendar

October 18, 2010
Monday, October 18
Geometry and Topology
Time: 15:30
Speaker: Rick Jardine (Western)
Title: "Dynamical systems and diagrams"
Room: MC 107

Abstract: A dynamical system is a map of spaces X×SX, and a map of dynamical systems XY over S is an S-equivariant map. There is both an injective and a projective model structure for this category.

These model structures are special cases of injective and projective model structures for space-valued diagrams X defined on a fixed category A enriched in simplicial sets. Simultaneously varying the parameter category A (or parameter space S) along with the diagrams X up to weak equivalence is more interesting, and requires new model structures for A-diagrams having weak equivalences defined by homotopy colimits, as well as a generalization of Thomason's model structure for small categories to a model structure for simplicial categories.