交换辛代数全轨道K-理论中的挠率
Torsion in the full orbifold K-theory of abelian symplectic quotients
摘要：
设（M，ω，Φ）是Hamilton T-空间，H是T的闭Lie子环面.在对矩映射Φ作一些技术性假设的情况下，证明了轨道辛商[M//H]的积分全轨道K-理论中不存在加挠.我们的主要技术工具是推广到矩映射水平集的情况，得到了著名的结果：哈密顿T-空间M的矩映射的分量是M上的Morse-Bott函数。作为第一个应用，我们得出结论，一个大类的辛复曲面orbifolds，以及某些S^1-的GKM空间，有积分完整的orbifolds K-理论，是免费的加挠。最后，我们引入半局部Delzant的概念，它使我们能够制定充分条件下的假设的主要定理。我们使用低秩共伴随轨道的类型A和B说明我们的结果。
英文摘要：
Let (M,ω,Φ) be a Hamiltonian T-space and let H be a closed Lie subtorus of T. Under some technical hypotheses on the moment map Φ, we prove that there is no additive torsion in the integral full orbifold K-theory of the orbifold symplectic quotient [M//H]. Our main technical tool is an extension to the case of moment map level sets the well-known result that components of the moment map of a Hamiltonian T-space M are Morse-Bott functions on M. As first applications, we conclude that a large class of symplectic toric orbifolds, as well as certain S^1-quotients of GKM spaces, have integral full orbifold K-theory that is free of additive torsion. Finally, we introduce the notion of semilocally Delzant which allows us to formulate sufficient conditions under which the hypotheses of the main theorem hold. We illustrate our results using low-rank coadjoint orbits of type A and B.
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