$\mathbf{R/Z}$ index theory

Index Theory

Lecture Notes taken by Nilufer Koldan In this lecture I will describe one of the most significant achievements of the second half of the XX century – the Atiyah-Singer index theorem. I will also discuss some more recent developments in the area as well as some open problems. 1. The definition of the index 1.1. The finite-dimensional case. Let A : V 1 → V 2 be a linear map between finite dimensi...

R/Z Index Theory

We define topological and analytic indices in R/Z K-theory and show that they are equal.

Enlargeability and index theory

Let M be a closed enlargeable spin manifold. We show nontriviality of the universal index obstruction in the K-theory of the maximal C-algebra of the fundamental group of M . Our proof is independent from the injectivity of the Baum-Connes assembly map for π1(M) and relies on the construction of a certain infinite dimensional flat vector bundle out of a sequence of finite dimensional vector bun...

Index Theory for Coverings

Equivariant KK-theory and noncommutative index theory