Chen-Ruan cohomology of M_{1,n} and \bar{M}_{1,n}

TL;DR

This paper computes the Chen-Ruan cohomology and stringy Chow ring of genus 1 moduli spaces, proposing a new orbifold tautological ring that bridges these structures and enhances understanding of their algebraic properties.

Contribution

It introduces a novel orbifold tautological ring for genus 1, connecting Chen-Ruan cohomology and stringy Chow ring in the context of moduli spaces.

Findings

Computed Chen-Ruan cohomology for M_{1,n} and ar{M}_{1,n}

Defined the orbifold tautological ring in genus 1

Proposed relationships between cohomology and Chow rings

Abstract

In this work we compute the Chen--Ruan cohomology and the stringy Chow ring of the moduli spaces of smooth and stable $n$-pointed curves of genus 1. We suggest a definition for an Orbifold Tautological Ring in genus 1, which is both a subring of the Chen--Ruan cohomology and of the stringy Chow ring.