The K-theory of abelian symplectic quotients
The K-theory of abelian symplectic quotients
复制标题
阿贝尔辛商的 K 理论
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
G. Landweber
中科院分区：
文献类型：
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作者：
M. Harada;G. Landweber
设T是一个紧环面，（M，ω）是
Hamilton T-空间在前一篇文章中，作者证明了在矩映射上，在一定的技术条件下，流形M的T-等变K-理论覆盖到M的辛商M mod T的常积分K-理论上。本文利用等变莫尔斯理论给出了一种计算辛商K-理论的方法，得到了满射kappa：K^*_T（M）到K^*（M mod T）上的核的显式描述.我们的结果是K-理论的类似物的工作托尔曼和魏茨曼Borel等变上同调。进一步，我们证明了在适当的技术条件下，M的T-轨道分层，存在一个显式的Goresky-Kottwitz-MacPherson（"GKM“）型组合描述的K-理论的Hamilton T-空间的不动点数据.最后，我们通过计算紧致辛环面流形的普通K-理论来说明我们的方法，紧致辛环面流形作为仿射空间C^N的辛对偶通过线性环面作用而产生。
Let T be a compact torus and (M,omega) a
Hamiltonian T-space. In a previous paper, the authors showed that the T-equivariant K-theory of the manifold M surjects onto the ordinary integral K-theory of the symplectic quotient M mod T of M by T, under certain technical conditions on the moment map. In this paper, we use equivariant Morse theory to give a method for computing the K-theory of the symplectic quotient by obtaining an explicit description of the kernel of the surjection kappa: K^*_T(M) onto K^*(M mod T). Our results are K-theoretic analogues of the work of Tolman and Weitsman for Borel equivariant cohomology. Further, we prove that under suitable technical conditions on the T-orbit stratification of M, there is an explicit Goresky-Kottwitz-MacPherson (``GKM') type combinatorial description of the K-theory of a Hamiltonian T-space in terms of fixed point data. Finally, we illustrate our methods by computing the ordinary K-theory of compact symplectic toric manifolds, which arise as symplectic quotients of an affine space C^N by a linear torus action.