Li-Sheng Tsai, UC Irvine

Title: Mapping cones of differential forms

Abstract: Many manifolds of interest are equipped with a geometrical structure represented by a distinguished closed differential form.  These include for example symplectic manifolds and manifolds with special holonomy.   For such spaces, we consider the mapping cone complex of the distinguished closed form mapping between two de Rham complexes by exterior product.  We will show that the resulting mapping cone cohomology groups represent novel invariants and have many interesting geometrical properties similar to those of the de Rham cohomology.  They also lead to new notions of Morse theory, flat connections, and Yang-Mills theories.