Morse theory on manifolds with boundary I. Strong Morse function, cellular structures and algebraic simplification of cellular differential
arXiv:1912.06437
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.
A chapter (3 pages) on estimation from below on a number of critical points of an extension of a strong Morse germ is added