A microlocal category associated to a symplectic manifold
A microlocal category associated to a symplectic manifold
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与辛流形相关的微局域范畴
DOI：
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发表时间：
2013
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通讯作者：
B. Tsygan
中科院分区：
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作者：
B. Tsygan
对于满足一定拓扑条件的辛流形，我们定义了变形量子代数上一类特殊的模。对于任意两个这样的模，我们构造一个无穷大的局部态射系统。我们从一个满足拓扑条件的拉格朗日子流形出发，构造了这样一个特殊的模。我们比较的结果莫尔斯理论，最近定义的Tamarkin层的微局部类别，和福谷类别的二维环面。几个附录解释了来自伪微分算子和分布的渐近分析的动机。
For a symplectic manifold satisfying some topological condition,we define a special class of modules over the deformation quantization algebra. For any two such modules we construct an infinity local system of morphisms. We construct such special module starting from a Lagrangian submanifold satisfying a topological condition. We compare the result to Morse theory, to the microlocal category of sheaves recently defined by Tamarkin, and to the Fukaya category of the two-dimensional torus. Several appendices explain the motivations that come from asymptotic analysis of pseudo-differential operators and distributions.