The topic of this book is 3-manifold groups, that is, fundamental groups of compact 3-
manifolds. This class of groups sits between the class of fundamental groups of surfaces …

Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological
quantum error correcting codes. They are low density parity check codes with linear rate and …

arxiv:1205.0202v3 [math.GT] 24 Apr 2013 Page 1 arxiv:1205.0202v3 [math.GT] 24 Apr 2013
3-MANIFOLD GROUPS MATTHIAS ASCHENBRENNER, STEFAN FRIEDL, AND HENRY …

In this paper we prove that, for any arithmetic hyperbolic n-manifold M of the first type, the
systole of most of the principal congruence coverings MI satisfy sys1. MI/8 nn C 1/log. vol …

We bound the-norm of an harmonic-form in an orientable cusped hyperbolic-manifold by its
topological complexity, measured by the Thurston norm, up to a constant depending on. This …

On Arithmetic Manifolds with Large Systole Page 1 INSTITUTO NACIONAL DE MATEMÁTICA
PURA E APLICADA DOCTORAL THESIS On Arithmetic Manifolds with Large Systole Plinio …

We study growth of absolute and homological k-dimensional systoles of arithmetic n-
manifolds along congruence coverings. Our main interest is in the growth of systoles of …

Let $ d $ be a square free positive integer and $\mathbb {Q}(\sqrt {d}) $ a totally real
quadratic field over $\mathbb {Q} $. We show there exists an arithmetic lattice L in $ SL …

We show that any closed hyperbolic 3-manifold M has a co-final tower of covers Mi! M of
degrees ni such that any subgroup of 1. Mi/generated by ki elements is free, where ki nC i …

arxiv:1911.01170v1 [math.MG] 4 Nov 2019 Page 1 arxiv:1911.01170v1 [math.MG] 4 Nov 2019
ON THE SYSTOLE GROWTH IN CONGRUENCE QUATERNIONIC HYPERBOLIC MANIFOLDS …