The age grading and the Chen-Ruan cup product

TL;DR

This paper demonstrates that the obstruction bundle in Chen-Ruan cohomology is determined by age grading, leading to a Kunneth Theorem and simplified proofs of properties like associativity.

Contribution

It shows that the obstruction bundle can be directly computed from age grading, simplifying the understanding of Chen-Ruan cohomology structures.

Findings

Obstruction bundle is determined by age grading.

Kunneth Theorem for Chen-Ruan cohomology established.

Simplified proofs for associativity and other properties.

Abstract

We prove that the obstruction bundle used to define the cup-product in Chen-Ruan cohomology is determined by the so-called `age grading' or `degree-shifting numbers'. Indeed, the obstruction bundle can be directly computed using the age grading. We obtain a Kunneth Theorem for Chen-Ruan cohomology as a direct consequence of an elementary property of the age grading, and explain how several other results - including associativity of the cup-product - can be proved in a similar way.