Torus Fibrations and Localization of Index II
Torus Fibrations and Localization of Index II
复制标题
环面纤维和索引 II 的定位
DOI：
10.1007/s00220-014-1890-7
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发表时间：
2014
影响因子：
2.4
通讯作者：
M.Furuta and T.Yoshida
中科院分区：
文献类型：
--
作者：
H. Fujita;M.Furuta and T.Yoshida
给出了开流形上dirac型算子索引的一个局部化框架。假设开流形有一个紧子集，它的补被有限多个开子集所覆盖，每个开子集都有一个环面束的总空间结构。在非循环条件下，利用witten型变形定义了dirac型算子的索引，并证明了该索引具有可切性和乘积公式等性质。特别地，我们证明了索引在紧集中是局部的。
We give a framework of localization for the index of a Dirac-type operator on an open manifold. Suppose the open manifold has a compact subset whose complement is covered by a family of finitely many open subsets, each of which has a structure of the total space of a torus bundle. Under an acyclic condition we define the index of the Dirac-type operator by using the Witten-type deformation, and show that the index has several properties, such as excision property and a product formula. In particular, we show that the index is localized on the compact set.