arXiv subjects

Martin D. Bobb

Publications and source records attributed to Martin D. Bobb.

2 recordsLinked to original sources

arXiv2020

Codimension-$1$ Simplices in Divisible Convex Domains

Properly embedded simplices in a convex divisible domain $Ω\subset \mathbb{R} \textrm{P}^d$ behave somewhat like flats in Riemannian manifolds, so we call them flats. We show that the set of codimension-$1$ flats has image which is a finite collection of disjoint virtual $(d-1)$-tori in the compact quotient manifold. If this collection of virtual tori is non-empty, then the components of its complement are cusped convex projective manifolds with type $d$ cusps.

math.GT↗

arXiv2019

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

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 $n$).

math.GT↗