### Spring 2009 MAT 541 Intemediate Algebraic Topology

### Dennis Sullivan

In MAT 540 we discussed the Eilenberg Steenrod axioms, which characterize the ordinary cohomology functor on finite polyhedra. In MAT 541 we will discuss the axioms that similarly characterize ordinary differential cohomology. This functor was introduced at Stony Brook in the seventies by Cheeger and Simons. Differential cohomology is the receiving space for an invariant of a vector bundle with connection that was invented to combine the integral characteristic classes of the vector bundle with the Chern Weil differential forms, defined by the curvature of the connection which represent the characteristic classes in real cohomology.