28 citations · 109 across the 24 of their papers we have counts for
31 papers
Local Connectivity of Right-angled Coxeter group boundaries
Michael Mihalik, Kim Ruane, Steve Tschantz
We provide conditions on the defining graph of a right-angled Coxeter group presentation that guarantees the boundary of any CAT(0) space on which the group acts geometrically will…
The geometry in Plato's Meno
John G. Ratcliffe, Sophia Stone, Steven T. Tschantz
In this paper, we analyze the two geometrical passages in Plato's Meno, (81c -- 85c) and (86e4 -- 87b2), from the points of view of a geometer in Plato's time and today. We give, i…
The G-index of a closed, spin, hyperbolic manifold of dimension 2 or 4
John G. Ratcliffe, Steven T. Tschantz
In this paper, we develop general techniques for computing the G-index of a closed, spin, hyperbolic 2- or 4-manifold, and apply these techniques to compute the G-index of the full…
The signature of cusped hyperbolic 4-manifolds
Alexander Kolpakov, Stefano Riolo, Steven T. Tschantz
In this note we show that every integer is the signature of a non-compact, oriented, hyperbolic 4-manifold of finite volume, and give some partial results on the geography of such…
Hyperbolic 24-cell 4-manifolds with one cusp
John G. Ratcliffe, Steven T. Tschantz
In this paper, we describe all the hyperbolic 24-cell 4-manifolds with exactly one cusp. There are four of these manifolds up to isometry. These manifolds are the first examples of…
Co-Seifert fibrations of compact flat 3-orbifolds
John G. Ratcliffe, Steven T. Tschantz
This paper is a continuation of our previous paper, Co-Seifert fibrations of compact flat orbifolds, in which we developed the theory for classifying geometric fibrations of compac…