Torus Fibrations and Localization of Index III
Torus Fibrations and Localization of Index III
复制标题
环面纤维和索引 III 的定位
DOI：
10.1007/s00220-014-2039-4
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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-型算子指数的局部化框架。假设开流形有一个紧致子集，它的补集被一族有限多个开子集所覆盖，每个开子集族都有一个环形丛的全空间的结构。在非循环条件下，利用Witten型变形定义了Dirac型算子的指数，并证明了指数具有截除性和乘积公式等性质。特别地，我们证明了该索引在紧集上是局部的。
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.