# nLab quantum sheaf cohomology

Contents

cohomology

### Theorems

#### Quantum field theory

functorial quantum field theory

# Contents

## Idea

Gromov-Witten theory may be understood as providing a product on formal power series over certain abelian sheaf cohomology groups of Kähler manifolds $X$. The quantum cohomology of $X$ is the resulting Frobenius algebra structure on these formal power series.

Together with Gromov-Witten theory quantum sheaf cohomlogy was discovered in and has its geometric roots as part of the data that describes certain 2-dimensional sigma-model quantum field theories with target space $X$.

## References

An introduction for readers familiar with basic concepts of Gromov-Witten theory is in

• Josh Guffin, Quantum sheaf cohomology, a précis (pdf)

Slides of a talk for an audience of mathematical string theorists are

• Quantum sheaf cohomology (pdf) Brandeis university (2010)

Quantum sheaf cohomology I (pdf)

Last revised on January 5, 2014 at 15:14:42. See the history of this page for a list of all contributions to it.