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An Introduction to Geometric Group Theory
Mikhail Belolipetsky, Gisele Teixeira Paula
This book provides a self-contained introduction to geometric group theory. The topics range from an introduction of Cayley and Schreier graphs to Gromov's theorem on groups of pol…
On multiplicities in length spectra of semi-arithmetic hyperbolic surfaces
Mikhail Belolipetsky, Gregory Cosac, Cayo Dória +1
We show that semi-arithmetic surfaces of arithmetic dimension two which admit a modular embedding have exponential growth of mean multiplicities in their length spectrum. Prior to…
A strong height gap theorem for
Mikhail Belolipetsky, Sebastian Hurtado
The height gap theorem states that the finite subsets of matrices generating non-virtually solvable groups have normalized height bounded below by a constant.…
Geometry and arithmetic of semi-arithmetic Fuchsian groups
Mikhail Belolipetsky, Gregory Cosac, Cayo Dória +1
Semi-arithmetic Fuchsian groups is a wide class of discrete groups of isometries of the hyperbolic plane which includes arithmetic Fuchsian groups, hyperbolic triangle groups, grou…