Seminário Análise Funcional e Aplicações 

19/01/2007, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Catarina Carvalho, Instituto Superior Técnico, U.T. Lisboa

The Fredholm index in $K$-theory for $C^{*}$-algebras

In this talk, I will give an introduction to index theory in the non-commutative geometry framework. $K$-theory for $C^{*}$-algebras will be developed, and it will be shown how one can associate $K$-theory classes to Fredholm operators, so that the Fredholm index arises as a map in $K$-theory. We will see also how this approach leads to generalized Fredholm indices, which do not take integer values, but instead take values in some $K$-theory group. One example of particular importance is that of families of operators.