Speaker: Kameron McCombs, Dartmouth College

Date: February 23, 2023

Abstract: In 1971 Atiyah and Singer created an index theory for families of elliptic operators, where a family of elliptic operators parametrized by a compact manifold Y is associated with an element of the K-theory of Y. Crucial to this result was the definition of a continuous family of Fredholm operators indexed by Y. In this talk, we will define a new class of operators on B(L^2M) for a compact manifold M called f-continuous operators in order to derive a new way to define a continuous family of Fredholm operators. This will allow us to more easily calculate the index of a continuous family of Fredholm operators.