Title: Equivariant and Fractional Analytic Index

Abstract: 
The A-hat genus is defined for any compact oriented manifold,
and is a topological invariant, but however not an integer in general.
I will report on some joint work with R.B. Melrose and I.M. Singer,
where we propose 2 solutions to the question as to what corresponds
to the analytic index when the A-hat genus is not an integer, and
also how we relate these solutions.