量子Steenrod方的构造及其代数关系
A construction of the quantum Steenrod squares and their algebraic relations
摘要：
在Chaanaya，Betz和Cohen的工作基础上，我们在闭单调辛流形上构造了Steenrod平方结构的量子变形.我们证明量子版本的Cartan和Adem关系。我们计算的量子Steenrod平方为所有CP n，并给出所有复曲面品种的计算手段。作为一个应用，我们还描述了两个例子的爆破沿一个子品种，其中一个量子校正的Steenrod平方爆破是由经典Steenrod平方的子品种。
英文摘要：
We construct a quantum deformation of the Steenrod square construction on closed monotone symplectic manifolds, based on the work of Fukaya, Betz and Cohen. We prove quantum versions of the Cartan and Adem relations. We compute the quantum Steenrod squares for all CP n and give the means of computation for all toric varieties. As an application, we also describe two examples of blowups along a subvariety, in which a quantum correction of the Steenrod square on the blowup is determined by the classical Steenrod square on the subvariety.
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