Chen-ruan Orbifold Cohomology of Weighted Projective Space
نویسنده
چکیده
Chen and Ruan [6] defined a very interesting cohomology theoryChen-Ruan orbifold cohomology. The primary objective of this paper is to compute the Chen-Ruan orbifold cohomology of weighted projective space, one of the most important space used in physics. The classical tools (orbifold cohomology defined by Chen and Ruan,toric varieties, the localization formula) which have been proved to be successful are used to study the orbifold cohomology of weighted projective space. We obtain the following: Given a weighted projective space P q0,··· ,qn , the twisted sectors and the degree shifting numbers of P q0,··· ,qn can be determined and calculated,so does the orbifold cohomology of P q0,··· ,qn ; For a general reduced weighted projective space, we give a method to compute its Chen-Ruan orbifold cohomology ring.
منابع مشابه
The Chen-ruan Orbifold Cohomology of Weighted Projective Spaces
Chen and Ruan [6] defined a very interesting cohomology theoryChen-Ruan orbifold cohomology. The primary objective of this paper is to compute the Chen-Ruan orbifold cohomology of the weighted projective spaces, one of the most important space used in physics. The classical tools (orbifold cohomology defined by Chen and Ruan, toric varieties, the localization technique) which have been proved t...
متن کاملChen-ruan Orbifold Cohomology of Weighted Projective Space 1
Chen and Ruan [6] defined a very interesting cohomology theory-Chen-Ruan orbifold cohomology. The primary objective of this paper is to compute the Chen-Ruan orbifold cohomology of weighted projective space, one of the most important space used in physics. The classical tools (orbifold cohomology defined by Chen and Ruan,toric varieties, the localization formula) which have been proved to be su...
متن کاملWeighted hyperprojective spaces and homotopy invariance in orbifold cohomology
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 hyperkähler quotients of T C by S (here termed weighted hyperprojective spaces) are homotopy equivalent to weighted projective spaces, they are not S-representat...
متن کاملOrbifold Cohomology of Torus Quotients
We introduce the inertial cohomology ring NH T (Y) of a stably almost complex manifold carrying an action of a torus T . We show that in the case that Y has a locally free action by T , the inertial cohomology ring is isomorphic to the Chen-Ruan orbifold cohomology ring H∗CR(Y/T ) (as defined in [Chen-Ruan]) of the quotient orbifold Y/T . For Y a compact Hamiltonian T -space, we extend to orbif...
متن کاملOrbifold cohomology of abelian symplectic reductions and the case of weighted projective spaces
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 weighted projective spaces. We start with a brief exposition of how orbifolds arise in the symplectic category, and discuss the techniques used to understand ...
متن کامل