On Topology of Carrying Manifolds of Regular Homeomorphisms

TL;DR

This paper explores the relationship between the topology of closed manifolds of dimension four or higher and the structure of non-wandering sets of regular homeomorphisms, focusing on Morse-Smale diffeomorphisms.

Contribution

It establishes new connections between manifold topology and the dynamics of regular homeomorphisms, especially Morse-Smale systems, in higher dimensions.

Findings

Identifies topological constraints on non-wandering sets

Describes the structure of carrying manifolds for regular homeomorphisms

Provides insights into Morse-Smale diffeomorphisms in high dimensions

Abstract

We describe interrelations between a topology structure of closed manifolds (orientable and non-orientable) of the dimension $n\geq 4$ and the structure of the non-wandering set of regular homeomorphisms, in particular, Morse-Smale diffeomorphisms.