Isaac Newton Institute for Mathematical Sciences

Eta invariant, boundaries and the determinant line bundle

Authors: Richard B. Melrose (MIT), Frederic Rochon (Stony Brook)

Abstract

We will discuss the definition of the eta invariant on manifolds with boundary using cusp suspended operators. This will be used to show that the (exponentiated) eta invariant of a family of elliptic operators trivialzes the determinant bunle of the associated family of operators on the boundary, giving a pseudodifferential generalization of a result of Dai and Freed.