Smooth structures on Morse trajectory spaces, featuring finite ends and associative gluing

TL;DR

This paper introduces elementary methods to construct manifold with corner structures and associative gluing maps on compactified Morse flow line spaces, including finite and infinite trajectories.

Contribution

It provides new elementary constructions for manifold with corner structures and associative gluing maps on Morse trajectory space compactifications.

Findings

Manifold with corner structures successfully constructed for Morse flow lines.

Associative gluing maps established on compactified Morse trajectory spaces.

Applicable to finite, half-infinite, and infinite Morse flow lines.

Abstract

We give elementary constructions of manifold with corner structures and associative gluing maps on compactifications of spaces of infinite, half infinite, and finite Morse flow lines.