Convex projective manifolds with a cusp of any non‐diagonalizable type

Abstract

Recent work of Ballas, Cooper, and Leitner identifies ( n + 1 ) types of n-dimensional convex projective cusps, one of which is the standard hyperbolic cusp. Work of Ballas–Marquis and Ballas–Danciger–Lee [Ballas, Danciger and Lee, ‘Convex projective structures on nonhyperbolic threemanifolds’,Geom. Topol. 22 (2018) 1593–1646] give examples of these exotic (non-hyperbolic) type cusps in dimension 3. Here an extension of the techniques of Ballas–Marquis shows the existence of all cusp types in all dimensions, except diagonalizable (type n) [Ballas, Cooper and Leitner, ‘Generalized cusps in real projective manifolds: classification’, Preprint, 2017, arXiv:1710.03132; Ballas and Marquis, ‘Properly convex bending of hyperbolic manifolds’, Preprint, 2016, arXiv:1609.03046].