2012/05/21 by Wen Lu, Lu, Wen
Computer Science · Mathematics · #53C21 #58E05 #Algebraic Topology (math.AT) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Topological and Geometric Data Analysis #math.AP #math.AT #math.DG #msc:53C21 #msc:58E05
paper · pdf · doi:10.48550/arxiv.1205.4665
20 pages
arxiv created 2012/05/21 · openalex publication_date 2012/05/21 · arxiv updated 2012/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Given a smooth compact manifold with boundary, we show that the subcomplex of the deformed de Rham complex consisting of eigenspaces of small eigenvalues of the Witten Laplacian is canonically isomorphic to the Thom-Smale complex constructed by Laudenbach. Our proof is based on Bismut-Lebeau's analytic localization techniques. As a by-product, we obtain Morse inequalities for manifolds with boundary.