Recursion relations in semirigid topological gravity

TL;DR

This paper explores a field theoretical model of topological gravity within semirigid geometry, emphasizing the role of cohomology and BRST symmetry, and reproduces key equations of pure topological gravity.

Contribution

It introduces a novel realization of topological gravity using semirigid geometry, linking cohomological structures with physical operators and reproducing fundamental equations.

Findings

Topological nature characterized by deRham and equivariant BRST cohomology

Reproduction of puncture and dilaton equations in the model

Most physical operators are BRST-exact, indicating topological invariance

Abstract

A field theoretical realization of topological gravity is discussed in the semirigid geometry context. In particular, its topological nature is given by the relation between deRham cohomology and equivariant BRST cohomology and the fact that all but one of the physical operators are BRST-exact. The puncture equation and the dilaton equation of pure topological gravity are reproduced, following reference \dil.