# nLab Mishchenko-Fomenko index theorem

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

The Mishchenko-Fomenko index theorem is a generalization of the Atiyah-Singer index theorem to differential operators on Hilbert module-bundles over some C*-algebra.

## References

The original English version of the original work is

• A.S. Mishchenko, A.T. Fomenko, The index of elliptic operators over C-algebras., Math. USSR, Izv. 15 (1980), 87–112.

A more explicit rederivation is in section 6.1 of

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