Abstract
Comparing to the construction of stringy cohomology ring of equivariant stable almost complex manifolds and its relation with the Chen-Ruan cohomology ring of the quotient almost complex orbifolds, the authors construct in this note a Chen-Ruan cohomology ring for a stable almost complex orbifold. The authors show that for a finite group G and a G-equivariant stable almost complex manifold X, the G-invariant part of the stringy cohomology ring of (X, G) is isomorphic to the Chen-Ruan cohomology ring of the global quotient stable almost complex orbifold [X/G]. Similar result holds when G is a torus and the action is locally free. Moreover, for a compact presentable stable almost complex orbifold, they study the stringy orbifold K-theory and its relation with Chen-Ruan cohomology ring.
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The authors thank the anonymous referee for careful reading and valuable suggestions to improve this paper.
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This work was supported by the National Natural Science Foundation of China (Nos. 11501393, 11626050, 11901069), Sichuan Science and Technology Program (No. 2019YJ0509), joint research project of Laurent Mathematics Research Center of Sichuan Normal University and V. C. & V. R. Key Lab of Sichuan Province, by Science and Technology Research Program of Chongqing Education Commission of China (No. KJ1600324) and Natural Science Foundation of Chongqing, China (No. cstc2018jcyjAX0465).
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Du, C., Li, T. Chen-Ruan Cohomology and Stringy Orbifold K-Theory for Stable Almost Complex Orbifolds. Chin. Ann. Math. Ser. B 41, 741–760 (2020). https://doi.org/10.1007/s11401-020-0231-8
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DOI: https://doi.org/10.1007/s11401-020-0231-8