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

TL;DR

This paper develops a cellular structure for compact manifolds with boundary using strong Morse functions, providing algebraic insights and addressing Arnold's question on critical points.

Contribution

It introduces a cellular structure based on strong Morse functions on manifolds with boundary and explores its algebraic properties, also estimating critical points for specific boundary conditions.

Findings

Constructed cellular structures for manifolds with boundary

Analyzed algebraic properties of the cellular structures

Provided estimates for critical points in boundary conditions

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.