# nLab Fredholm index

Contents

### Context

#### Index theory

index theory, KK-theory

noncommutative stable homotopy theory

partition function

genus, orientation in generalized cohomology

## Definitions

operator K-theory

K-homology

# Contents

## Idea

A Fredholm operator $F \,\colon\, \mathcal{H} \longrightarrow \mathcal{H}$ by definition has finite-dimensional kernel $ker(F)$ and cokernel $coker(F)$. Its index is the difference between these dimensions:

$ind(F) \;\coloneqq\; dim\big(ker(F)\big) \,-\, dim\big(coker(F)\big) \,.$

## References

Textbook account:

• William Arveson, Section 3.4 of: A Short Course on Spectral Theory, Graduate Texts in Mathematics 209 $[$doi:10.1007/b97227$]$

Created on May 9, 2022 at 02:57:02. See the history of this page for a list of all contributions to it.