论文标题
持续共同体学和pforms的Arrhenius法律的条形法规
Bar codes of persistent cohomology and Arrhenius law for p-forms
论文作者
论文摘要
本文表明，可以在半古典限制中计算或计算Witten Laplacian的小特征值，而无需假设潜力是莫尔斯的功能，就像作者在[LNV]中所做的那样。与持续的同胞学有关，我们证明了这些小特征值的重新对数是由函数f的条形码f的长度渐近确定的。特别是，这证明了这些数量在函数空间的C 0拓扑中是稳定的。此外，我们的分析提供了一种在大量情况下计算次指数校正的一般方法。
This article shows that counting or computing the small eigenvalues of the Witten Laplacian in the semi-classical limit can be done without assuming that the potential is a Morse function as the authors did in [LNV]. In connection with persistent cohomology, we prove that the rescaled logarithms of these small eigenvalues are asymptotically determined by the lengths of the bar code of the function f. In particular, this proves that these quantities are stable in the C 0 topology on the space of functions. Additionally, our analysis provides a general method for computing the subexponential corrections in a large number of cases.
