4 citations · 7 across the 3 of their papers we have counts for
8 papers
Nonvanishing of algebraic entropy for geometrically finite groups of isometries of Hadamard manifolds
Roger C. Alperin, Guennady A. Noskov
We prove that any geometrically finite (nonelementary) group of isometries of a pinched Hadamard manifold has uniform exponential growth.
Trisections and Totally Real Origami
Roger C. Alperin
We introduce a trisection axiom for mathematical origami and descibe the totally real origami numbers. We also discuss the solution of Alhazen's problem and its relation to trisect…
Separability of Solvable Subgroups in Linear Groups
Roger Alperin, Benson Farb
Let G be a finitely generated linear group over a field of characteristic 0. Suppose that every solvable subgroup of G is polycyclic. Then the claim is made that any solvable subgr…
Uniform Growth, Actions on Trees and
Roger C. Alperin, Guennadi A. Noskov
We use actions on trees to determine uniform exponential growth for subgroups of .
A strong Schottky Lemma for nonpositively curved singular spaces
Roger C. Alperin, Benson Farb, Guennadi A. Noskov
In this paper we give a criterion for pairs of isometries of a nonpositively curved metric space to generate a free group. This criterion holds only in singular spaces, for example…
The Modular Tree of Pythagorus
Roger C. Alperin
The Pythagorean triples have the structure of a ternary rooted tree; the tree is based on the Cayley graph of a free subgroup of the modular group