A new approach in index theory

online | | 14:30

Mohammed Berkani

University Mohammed I


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.  

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