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Systoles of Arithmetic Hyperbolic 2- and 3-Manifolds
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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.
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Title: Systoles of Arithmetic Hyperbolic 2- and 3-Manifolds
Description:
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.
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