# A new approach in index theory

### online | 2021-11-11 | 14:30

Mohammed Berkani

University Mohammed I

https://videoconf-colibri.zoom.us/j/9301932415

Title: A new approach in index theory

Abstract: In this talk,  we define an analytical index for a continuous family of Fredholm operators parameterized by a topological space X into a Hilbert space H, as a sequence of integers, avoiding in this way  the use of K-theory as in the work of Atiyah-Singer and  extending naturally the usual definition of the index. Then  we prove the homotopy invariance of the index and we give an Atiyah-Janich type theorem in the case where $X$ is a compact, locally connected space.  Extension to the case of Banach spaces will be discussed and several open questions will be pointed out.