# nLab topological chiral homology

cohomology

### Theorems

#### Higher algebra

higher algebra

universal algebra

# Contents

## Idea

Topological chiral homology is a generalization of Hochschild homology. Where Hochschild homology is given by (∞,1)-colimits of functors constant on an $\infty$-algebra over a diagram that is an ∞-groupoid, topological chiral homology is given by colimits of constant functors over (∞,1)-categories of open subsets of a manifold.

This generalizes the concept of chiral homology by Beilinson-Drinfeld.

## Definition

For the moment see the section Topological chiral homology at the entry on Hochschild homology.

The notion of topological chiral homology should be closely related to that of

and be related to concepts in

Other related concepts

## References

A quick definition and comments on its relation to FQFT are in section 4.1 of

Technical details are in section 3 of

which meanwhile has becomes part of section 5 of

Revised on July 6, 2013 00:35:58 by Urs Schreiber (89.204.130.15)