Séance Séminaire

Séminaire des Doctorant·e·s

Γ - Fredholm operator

Let D be an elliptic differential operator. One might hope to find the solutions of the equation Df = 0 but this is almost impossible. This is where the index play a crucial role and can give us information about the number of solutions of such an equation. In this talk I will present the importance of the analytical index of an elliptic differential Fredholm operator. Then I will briefly give an idea about the Atiyah-Singer Theorem on compact manifold. In a second part I will explain the notion of Γ-Fredholm operator relative to the group Von Neumann algebra. Finally, I will give suffcient condition for a Dirac operator on complete manifold to be Γ-Fredholm.