Shellings of tropical hypersurfaces

In this talk we investigate the shellability of the boundary complex of an unbounded polyhedron. For this concept to make sense, it is necessary to pass to a suitable compactification, e.g., by one point. This can be exploited to prove that any tropical hypersurface is shellable. Under the hood there is a subtle interplay between the duality of polyhedral complexes and shellability. Translated into discrete Morse theory, that interplay entails that the tight span of an arbitrary regular subdivision is collapsible, not not shellable in general.

This talk is based on joint work with George Balla and Michael Joswig.