Noncommutative Geometry Seminar

Date: September 12, 2018

Time: 2:00PM - 3:00PM

Location: BLOC 628

Speaker: Hao Guo, Texas A&M University

Title: Index of Equivariant Callias-Type Operators

Abstract: I will discuss a class of Dirac-type operators, called equivariant Callias-type operators, on manifolds equipped with a Lie group action, where the orbit space is non-compact. It turns out that these operators are Fredholm with an index in the K-theory of the group C*-algebra and can be constructed by adding an ordinary (non-Fredholm) Dirac operator to an element of the K-theory of the equivariant Higson corona of the manifold. One can apply the index theory of such operators to prove an obstruction theorem for invariant metrics of positive scalar curvature.