Resurgent analysis of the Witten Laplacian in one dimension -- II

Alexander Getmanenko

Published 2010-04-19, updated 2012-04-02Version 2

The Witten Laplacian in one dimension is studied further by methods of resurgent analysis in order to approach Fukaya's conjectures relating WKB asymptotics and disc instantons. In this paper more precise connection formulae are presented, which allows the calculation of a subdominant exponential term in the hyperasymptotic expansion of a low-lying eigenvalue. Calculation of eigenfunctions corresponding to low-lying eigenvalues is presented in two examples.