TITLE: Triangulations of submanifolds of smooth manifolds
QUESTION [8 upvotes]: Every smooth manifold $M$ has a PL structure, and therefore a triangulation. Given a submanifold $N$ of $M$, does anyone know some nice conditions for $N$ to be the subcomplex of some triangulation of $M$, or isotopic to one?

REPLY [8 votes]: It follows from Verona's solution to Thom's triangulation conjecture that the inclusion $N\hookrightarrow M$ is triangulable whenever it is proper and topologically stable, and $M$ and $N$ are without boundary.
Verona, Andrei, Stratified mappings - structure and triangulability, Lecture Notes in Mathematics. 1102. Subseries: Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn, Vol. 4. Berlin etc.: Springer-Verlag. IX, 160 p. DM 26.50 (1984) ZBL0543.57002.