2019/01/31 by Chengyuan Wu, Shiquan Ren, Jie Wu +1
Computer Science · Mathematics · #Algebra over a field #Cellular homology #Circle-valued Morse theory #Combinatorics #Computer science #Discrete Morse theory #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Morse code #Morse homology #Morse theory #Pure mathematics #Simplicial complex #Simplicial homology #Singular homology #Topological and Geometric Data Analysis #Topology (electrical circuits) #math.AT
paper · pdf · doi:10.1016/j.topol.2019.107038
published as Topology and its Applications 270 (2020): 107038 · 19 pages, to appear in Topology and its Applications
arxiv created 2019/12/10 · openalex publication_date 2019/12/16 · arxiv updated 2020/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we study Forman's discrete Morse theory in the context of weighted homology. We develop weighted versions of classical theorems in discrete Morse theory. A key difference in the weighted case is that simplicial collapses do not necessarily preserve weighted homology. We work out some sufficient conditions for collapses to preserve weighted homology, as well as study the effect of elementary removals on weighted homology. An application to sequence analysis is included, where we study the weighted ordered complexes of sequences.