Weighted hyperprojective spaces and homotopy invariance in orbifold cohomology

Details Weighted hyperprojective spaces and homotopy invariance in orbifold cohomology Weighted hyperprojective spaces and homotopy invariance in orbifold cohomology

2007-08-16

arxiv.org/abs/0708.2278v1

Toric topology, 99--110, Contemp. Math., 460, Amer. Math. Soc., Providence, RI, 2008.

Mathematics

Symplectic Geometry

11 pages. To appear in AMS Contemporary Mathematics (Proceedings of the Toric Topology Conference, Osaka, Japan (May-June, 200

Scientific paper

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 hyperkahler quotients of the cotangent bundle to a complex vector space by a circle S^1 (here termed weighted hyperprojective spaces) are homotopy equivalent to weighted projective spaces, they are not S^1-representation homotopic. Indeed, we show that their Chen-Ruan cohomology rings (over the rationals) are distinct.

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