14 citations · 51 across the 19 of their papers we have counts for
24 papers
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…
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…
Cusp transitivity in hyperbolic 3-manifolds
John G. Ratcliffe, Steven T. Tschantz
In this paper, we study multiply transitive actions of the group of isometries of a cusped finite-volume hyperbolic 3-manifold on the set of its cusps. In particular, we prove a co…
Harmonic spinors on the Davis hyperbolic 4-manifold
John G. Ratcliffe, Daniel Ruberman, Steven T. Tschantz
In this paper we use the G-spin theorem to show that the Davis hyperbolic 4-manifold admits harmonic spinors. This is the first example of a closed hyperbolic 4-manifold that admit…