nLab
Fredholm module

Context

Index theory

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

For AA a C-star algebra, an odd Fredholm module over AA is a representation π:A()\pi : A \to \mathcal{B}(\mathcal{H}) of AA on a Hilbert space \mathcal{H} together with a Fredholm operator FF on \mathcal{H} such that [F,π(a)]𝒦()[F,\pi(a)] \in \mathcal{K}(\mathcal{H}) for all aAa \in A.

(…)

(Here ()\mathcal{B}(-) denotes bounded operators and 𝒦()\mathcal{K}(-) denotes compact operators).

A Fredholm module defines a class in K-homology, hence in KK-theory.

Last revised on March 17, 2017 at 03:27:57. See the history of this page for a list of all contributions to it.