Ruan's conjecture on orbifold symplectic flops

Let XX and YY be orbifolds related by an orbifold symplectic flop. The orbifold quantum cohomology rings are denoted by QHCR(X)QH^\ast_{CR}(X) and QHCR(Y)QH^\ast_{CR}(Y). Ruan's conjecture. If YY is the orbifold symplectic flop of XX, then

QHCR(X)QHCR(Y).QH^\ast_{CR}(X)\cong QH^\ast_{CR}(Y).

This conjecture asks whether orbifold quantum cohomology is invariant under orbifold symplectic flops, extending the corresponding transformation result for smooth flops. The source presents it as a proposed analogue of Ruan's conjecture; its resolution is not specified here.

Sources & referencesView supporting material

Primary source

Bohui Chen, An-Min Li, Qi Zhang and Guosong Zhao, “Singular symplectic flops and Ruan cohomology”, arXiv:0804.3144 (2008).

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