The spectral localizer for even index pairings
The spectral localizer for even index pairings
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DOI：
10.4171/jncg/357
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发表时间：
2018-02
影响因子：
0.9
通讯作者：
T. Loring;H. Schulz-Baldes
中科院分区：
文献类型：
--
作者：
T. Loring;H. Schulz-Baldes
偶指数对是将偶Fredholm模和由投影指定的$K_0$-类组合在一起的整数值同伦不变量。在微分和非对易几何和物理学中，有许多经典的例子。这里给出了如何构造一个有限维的自伴可逆矩阵，称为谱局部化子，使得它的签名的一半等于偶数索引对。这使得不变量在数值上是可访问的。指数论证明大量使用了模糊球。
Even index pairings are integer-valued homotopy invariants combining an even Fredholm module with a $K_0$-class specified by a projection. Numerous classical examples are known from differential and non-commutative geometry and physics. Here it is shown how to construct a finite dimensional selfadjoint and invertible matrix, called the spectral localizer, such that half its signature is equal to the even index pairing. This makes the invariant numerically accessible. The index-theoretic proof heavily uses fuzzy spheres.