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摘要翻译：
我们回顾并简化了我们以前的结果和Y.Ostrover关于半单量子同调辛流形上Calabi准态射和辛准态存在性的结果。作为说明，我们讨论了辛多环Fano 4-流形的情形。我们也给出了D.McDuff的新结果：她观察到对于准态射/准态的存在，只要假定量子同调包含一个场作为直和就足够了，并证明了这个较弱的条件对于非无扰辛流形的一点爆破成立。
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英文标题：
《Symplectic quasi-states and semi-simplicity of quantum homology》
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作者：
Michael Entov and Leonid Polterovich
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Symplectic Geometry 辛几何
分类描述：Hamiltonian systems, symplectic flows, classical integrable systems
哈密顿系统，辛流，经典可积系统
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We review and streamline our previous results and the results of Y.Ostrover on the existence of Calabi quasi-morphisms and symplectic quasi-states on symplectic manifolds with semi-simple quantum homology. As an illustration, we discuss the case of symplectic toric Fano 4-manifolds. We present also new results due to D.McDuff: she observed that for the existence of quasi-morphisms/quasi-states it suffices to assume that the quantum homology contains a field as a direct summand, and she showed that this weaker condition holds true for one point blow-ups of non-uniruled symplectic manifolds.
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PDF链接：
https://arxiv.org/pdf/0705.3735
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