6 citations · 9 across the 7 of their papers we have counts for
8 papers
Hyperbolic punctured spheres without arithmetic systole maximizers
Grant S. Lakeland, Clayton Young
We find bounds for the length of the systole -- the shortest essential, non-peripheral closed curve -- for arithmetic punctured spheres with cusps, for through , so…
Cheeger constants of hyperbolic reflection groups and Maass cusp forms of small eigenvalues
Brian A. Benson, Grant S. Lakeland, Holger Then
We compute the Cheeger constants of a collection of hyperbolic surfaces corresponding to maximal non-compact arithmetic Fuchsian groups, and to subgroups which are the rotation sub…
Hyperbolic triangular prisms with one ideal vertex
Grant S. Lakeland, Corinne G. Roth
In this paper, we classify all of the five-sided three-dimensional hyperbolic polyhedra with one ideal vertex, which have the shape of a triangular prism. We show how to find each…
The mod 2 cohomology rings of congruence subgroups in the Bianchi groups
Ethan Berkove, Grant Lakeland, Alexander Rahm +2
We provide new tools for the calculation of the torsion in the cohomology of congruence subgroups in the Bianchi groups : An algorithm for finding particularly useful fundamental d…
Strict contractions and exotic SO_0(d,1) quotients
Grant S. Lakeland, Christopher J Leininger
For d < 5, we describe an elementary construction of nonzero degree, strict contractions between closed, oriented hyperbolic d-oribifolds. Appealing to work of Gueritaud-Kassel and…
Equivalent trace sets for arithmetic Fuchsian groups
Grant S. Lakeland
We show that the modular group has an infinite family of finite index subgroups, each of which has the same trace set as the modular group itself. Various congruence subgroups of t…
Systoles and Dehn surgery for hyperbolic 3-manifolds
Grant S. Lakeland, Christopher J. Leininger
Given a closed hyperbolic 3-manifold M of volume V, and a link L in M such that the complement M \ L is hyperbolic, we establish a bound for the systole length of M \ L in terms of…
Dirichlet-Ford Domains and Arithmetic Reflection Groups
Grant S. Lakeland
In this paper, it is shown that a Fuchsian group, acting on the upper half-plane model for , admits a Ford domain which is also a Dirichlet domain, for some center, i…