Related papers: The Chen-Ruan Cohomology of Weighted Projective Sp…

These notes accompany a lecture about the topology of symplectic (and other) quotients. The aim is two-fold: first to advertise the ease of computation in the symplectic category; and second to give an account of some new computations for…

We compare the Chen-Ruan cohomology ring of the weighted projective spaces $\IP(1,3,4,4)$ and $\IP(1,...,1,n)$ with the cohomology ring of their crepant resolutions. In both cases, we prove that the Chen-Ruan cohomology ring is isomorphic…

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…

Comparing to the Chen-Ruan cohomology theory for the almost complex orbifolds, we study the orbifold cohomology theory for almost contact orbifolds. We define the Chen-Ruan cohomology group of any almost contact orbifold. Using the methods…

Let $(X,\,D)$ be an $m$-pointed compact Riemann surface of genus at least $2$. For each $x \,\in\, D$, fix full flag and concentrated weight system $\alpha$. Let $P \mathcal{M}_{\xi}$ denote the moduli space of semi-stable parabolic vector…

We describe the integral equivariant cohomology ring of a weighted projective space in terms of piecewise polynomials, and thence by generators and relations. We deduce that the ring is a perfect invariant, and prove a Chern class formula…

We prove the cohomological crepant resolution conjecture of Ruan for the weighted projective space P(1,3,4,4). To compute the quantum corrected cohomology ring we combine the results of Coates-Corti-Iritani-Tseng on P(1,1,1,3) and our…

We show that Chen-Ruan cohomology is a homotopy invariant in certain cases. We introduce the notion of a T-representation homotopy, which is a stringent form of homotopy under which Chen-Ruan cohomology is invariant. We show that while…

We give formulae for the Chen-Ruan orbifold cohomology for the orbifolds given by a Bianchi group acting on complex hyperbolic 3-space. The Bianchi groups are the arithmetic groups PSL\_2(A), where A is the ring of integers in an imaginary…

We present a deRham model for Chen-Ruan cohomology ring of abelian orbifolds. We introduce the notion of \emph{twist factors} so that formally the stringy cohomology ring can be defined without going through pseudo-holomorphic orbifold…

We compute the Chen-Ruan orbifold cohomology ring of the Batyrev mirror orbifold of a smooth quintic hypersurface in 4-dimensional projective space. We identify the obstruction bundle for this example by using the Riemann bilinear relations…

Chen and Ruan's orbifold cohomology of the symmetric product of a complex manifold is calculated. An isomorphism of rings (up to a change of signs) $H_{orb}^*(X^n/S_n;\complex) \cong H^*(X^{[n]};\complex)$ between the orbifold cohomology of…

We compute the integral torus-equivariant cohomology ring for weighted projective space for two different torus actions by embedding the cohomology in a sum of polynomial rings $\oplus_{i=0}^n \Z[t_1, t_2,..., t_n]$. One torus action gives…

In this work we describe the Chen-Ruan cohomology of the moduli stacks of smooth and stable genus 2 pointed curves, and its algebraic counterpart: the stringy Chow ring. In the first half of the paper we compute the additive structure of…

The purpose of this note is to give an overview of our work on defining algebraic counterparts for W. Chen and Y. Ruan's Gromov-Witten Theory of orbifolds. This work will be described in detail in a subsequent paper. The presentation here…

We compute the cohomological Brauer groups of twists of weighted projective spaces and weighted projective stacks.

This article is a revised, short and english version of my PhD thesis. First, we show a mirror theorem : the Frobenius manifold associated to the orbifold quantum cohomology of weighted projective space is isomorphic to the one attached to…

For any (n+1)-dimensional weight vector {\chi} of positive integers, the weighted projective space P(\chi) is a projective toric variety, and has orbifold singularities in every case other than CP^n. We study the algebraic topology of…

Let X be a compact connected Riemann surface of genus at least two. We compute the Chen--Ruan cohomology ring of the moduli space of stable PSL(2, C)--bundles of nontrivial second Stiefel--Whitney class over X.

We calculate the small quantum orbifold cohomology of arbitrary weighted projective spaces. We generalize Givental's heuristic argument, which relates small quantum cohomology to S^1-equivariant Floer cohomology of loop space, to weighted…