Orbifold cohomology of torus quotients

摘要: We introduce the inertial cohomology ring NHT*,◊(Y) of a stably almost complex manifold carrying an action torus T. show that in case where Y has locally free by T, is isomorphic to Chen-Ruan orbifold HCR*(Y/T) (as defined [CR]) quotient Y/T. For compact Hamiltonian T-space, we extend two techniques are standard ordinary cohomology. natural surjection onto HCR*(Y//T), Y//T symplectic reduction T at regular value moment map. graphical Goresky-Kottwitz-MacPherson (GKM) calculus detailed in, e.g., [HHH]) and kernel computations [TW] [G1], [G2]. detail this technology examples: toric orbifolds weight varieties, which reductions flag manifolds. The been computed for orbifolds, with Q-coefficients, [BCS]; reproduce their results over Q all obtained connected (though different computational methods) them Z-coefficients certain cases, including weighted projective spaces