Algebra/Topology seminar

Speaker: David Carchedi (George Mason University)

Titel: Dg-manifolds and a universal property for derived manifolds

Abstract: Given two smooth maps of manifolds f: M → L and g: N → L, if they are not transverse, the fibered product M x_L N may not exist, or may not have the correct cohomological properties. Thus lack of transversality obstructs many natural constructions in topology and differential geometry. Derived manifolds generalize the concept of smooth manifolds to allow arbitrary (iterative) intersections to exist as smooth objects, regardless of transversality. In this talk we will describe recent progress of ours with D. Roytenberg on giving an accessible geometric model for derived manifolds using differential graded manifolds. We will also discuss a universal property of derived manifolds, and recent progress as to how this concrete model satisfies this property.