与Spin Chern数有关的定量K理论
Quantitative K-Theory Related to Spin Chern Numbers
摘要：
我们研究了几乎可交换的酉矩阵对上定义的各种指数，这些指数可以检测到远离可交换对的对。我们这样做，在两个对称类，一般的酉矩阵和自对偶矩阵，强调定量的结果。我们确定哪些价值观的规范的换向器保证指数的定义，在那里他们是平等的，以及什么量化的结果的距离对不同的指数是可能的。我们验证了一种计算自旋陈数的方法，该方法是与黑斯廷斯一起开发的，并且只被证明是正确的。具体地说，Pfwean-Bott指数可以通过对换位子范数的“对数方法”计算到特定常数。
英文摘要：
We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this in two symmetry classes, that of general unitary matrices and that of self-dual matrices, with an emphasis on quantitative results. We determine which values of the norm of the commutator guarantee that the indices are defined, where they are equal, and what quantitative results on the distance to a pair with a different index are possible. We validate a method of computing spin Chern numbers that was developed with Hastings and only conjectured to be correct. Specifically, the Pfaffian-Bott index can be computed by the "log method" for commutator norms up to a specific constant.
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