# f-Continuous operators on B(L^2M) and the families index

** 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*^2

*M*) 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.