关于Cappell-Lee-Miller胶合定理
On the Cappell-Lee-Miller glueing theorem
摘要：
我们制定了一个更概念性的解释Cappell-Lee-Miller胶合/分裂定理使用新的语言的渐近映射和渐近精确性。此外，我们提出了一个渐近描述的迈尔-Vietoris序列自然相关的切赫上同调层的狄拉克型算子的局部解。我们讨论了在规范理论问题中经常出现的本征值估计、阻塞丛的近似和行列式线丛的胶合等问题的应用。所有这些结果中涉及的算子不必是平移不变的。
英文摘要：
We formulate a more conceptual interpretation of the Cappell-Lee-Miller glueing/splitting theorem using the new language of asymptotic maps and asymptotic exactness. Additionally, we present an asymptotic description of the Mayer-Vietoris sequence naturally associated to the Cech cohomology of the sheaf of local solutions of a Dirac type operator. We discuss applications to eigenvalue estimates, approximation of obstruction bundles and glueing of determinant line bundles frequently arising in gauge theoretic problems. The operators involved in all these results need not be translation invariant.
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