Morse theory on manifolds with boundary I. Strong Morse function, cellular structures and algebraic simplification of cellular differential

2019/12/13 by Petr E. Pushkar, Pushkar, Petr E.
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1912.06437

openalex publication_date 2019/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Main subject of the paper is a (strong) Morse function on a compact manifold with boundary. We construct a cellular structure and discuss its algebraic properties in this paper. Also we get an estimation on Arnold's question on a number of critical points of a Morse function with given boundary condition.

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