Smooth structures on Morse trajectory spaces, featuring finite ends and associative gluing (Q2845405)

The purpose of this long and technical paper is very well described in the 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. In the case of Euclidean metric in Morse coordinates near each critical point, these are naturally given by evaluations at end points and regular level sets. For finite ends this requires a blowup construction near trajectories ending at critical points.'' NEWLINENEWLINENEWLINEThe paper is organized into five chapters as follows: 1. Introduction; 2. Morse trajectory spaces, global charts, associative gluing (compactified Morse trajectory spaces, global charts, associative gluing maps); 3. Geometry and topology of Morse trajectory spaces; 4. Restrictions to local and connecting trajectories spaces (trajectories near critical points, restrictions to local trajectory spaces, connecting trajectory spaces and fibered products); 5. Gobal charts for Morse trajectory spaces (domains and targets, construction of a global chart for \(k=0\), construction of a global chart for \(k=1\) with end conditions \(\mathcal{Q}_0=\widetilde{U}(q_1)=\mathcal{Q}_2\), evaluation and transition times, construction of a general global chart, tubular neighborhoods of subspaces of maximally broken trajectories, construction for breaking number \(b=0\), construction for \(b\geq 1\) based on the construction for \(b-1\)). NEWLINENEWLINENEWLINEThe paper ends with a useful relevant bibliography of \(23\) references.NEWLINENEWLINEFor the entire collection see [Zbl 1253.00022].