2011/02/28 by David T. Gay, David T Gay, Robion Kirby · 11 citations
Computer Science · Mathematics · #Circle-valued Morse theory #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Morse code #Morse theory #Set (abstract data type) #Topological and Geometric Data Analysis #Uniqueness #math.DG #math.GT #msc:57M50 #msc:57R17 #msc:57R45
paper · pdf · doi:10.2140/gt.2015.19.2465
published in Geometry & Topology 19(5), 2465-2534 (Mathematical Sciences Publishers) · 74 pages, 41 figures; further errors corrected, some exposition added, other exposition improved, following referee's comments
arxiv created 2014/07/02 · openalex publication_date 2015/10/20 · arxiv updated 2016/01/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A Morse [math] –function is a generic smooth map from a smooth manifold to a surface. In the absence of definite folds (in which case we say that the Morse [math] –function is indefinite), these are natural generalizations of broken (Lefschetz) fibrations. We prove existence and uniqueness results for indefinite Morse [math] –functions mapping to arbitrary compact, oriented surfaces. “Uniqueness” means there is a set of moves which are sufficient to go between two homotopic indefinite Morse [math] –functions while remaining indefinite throughout. We extend the existence and uniqueness results to indefinite, Morse [math] –functions with connected fibers.