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 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 $n$).

arXiv comment21 pages, 7 figures

References in corpus (8)

• Introduction to Arithmetic Groups
• Convex projective structures on non-hyperbolic three-manifolds
• Peripheral separability and cusps of arithmetic hyperbolic orbifolds
• Generalized Cusps in Real Projective Manifolds: Classification
• Deforming convex projective manifolds
• Linear groups - Malcev's theorem and Selberg's lemma
• Collisions at infinity in hyperbolic manifolds
• Constructing convex projective 3-manifolds with generalized cusps

Cited by in corpus (4)

• Generalized Cusps in Real Projective Manifolds: Classification
• Codimension-$1$ Simplices in Divisible Convex Domains
• Divisible convex sets with properly embedded cones
• Constructing convex projective 3-manifolds with generalized cusps