2022/04/13 by Laurel Heck, Heck, Laurel, Benjamin Linowitz +1
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2204.06530
In this paper we study the systoles of arithmetic hyperbolic 2- and 3-manifolds. Our first result is the construction of infinitely many arithmetic hyperbolic 2- and 3-manifolds which are pairwise noncommensurable, all have the same systole, and whose volumes are explicitly bounded. Our second result fixes a positive number x and gives an upper bound for the least volume of an arithmetic hyperbolic 2- or 3-manifold whose systole is greater than x. We conclude by determining, for certain small values of x, the least volume of a principal arithmetic hyperbolic 2-manifold over Q or 3-manifold over Q(i) whose systole is greater than x.