偶指数对的谱定位子
The spectral localizer for even index pairings
摘要：
偶指数对是将偶Fredholm模与由投影指定的$K_0$类组合的整数值同伦不变量。许多经典的例子是已知的微分和非交换几何和物理。在这里，它是如何构建一个有限维的自伴和可逆矩阵，称为频谱定位器，使其一半的签名是等于偶指数配对。这使得不变量在数值上是可访问的。索引理论证明大量使用模糊球。
英文摘要：
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.
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