2014/08/17 by Joa Weber · 6 citations
Computer Science · Mathematics · #3-manifold #Algebra over a field #Cellular homology #Cohomology #Computer science #Flow (mathematics) #Geometric and Algebraic Topology #Geometry #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Isomorphism (crystallography) #Loop space #Mathematical analysis #Mathematics #Morse code #Morse homology #Morse theory #Pure mathematics #Riemannian manifold #Singular homology #Topological and Geometric Data Analysis #Triviality #math.AP #math.AT #math.DG #math.DS #msc:37L05 #msc:53C43 #msc:58E10 #msc:58J35
paper · pdf · doi:10.2422/2036-2145.201510_017
published in ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 853-909 · 54 pages, 14 figures
arxiv created 2014/08/17 · openalex publication_date 2017/09/21 · arxiv updated 2017/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In case of the heat flow on the free loop space of a closed Riemannian manifold non-triviality of Morse homology for semi-flows is established by constructing a natural isomorphism to singular homology of the loop space. The construction is also new in finite dimensions. The main idea is to build a Morse filtration using Conley pairs and their pre-images under the time-T-map of the heat flow. A crucial step is to contract each Conley pair onto its part in the unstable manifold. To achieve this we construct stable foliations for Conley pairs using the recently found backward λ-Lemma [31]. These foliations are of independent interest [23].