Two-dimensional topological gravity and equivariant cohomology

TL;DR

This paper explores the relationship between two-dimensional topological gravity and equivariant cohomology, revealing that the latter possesses a gravity algebra structure within topological conformal field theories.

Contribution

It introduces the concept of a gravity algebra in the context of equivariant cohomology of topological conformal field theories, establishing a new algebraic framework.

Findings

Equivariant cohomology carries a gravity algebra structure.

The analogy between topological string theory and equivariant cohomology is elucidated.

Correction of an error regarding the BRS current on page 9.

Abstract

In this paper, we examine the analogy between topological string theory and equivariant cohomology. We also show that the equivariant cohomology of a topological conformal field theory carries a certain algebraic structure, which we call a gravity algebra. (Error on page 9 corrected: BRS current contains total derivatives.)