Systolic volume of hyperbolic manifolds and connected sums of manifolds |
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Authors: | Stéphane Sabourau |
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Affiliation: | (1) Laboratoire de Mathématiques et Physique Théorique, Université de Tours, Parc de Grandmont, 37400 Tours, France |
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Abstract: | The systolic volume of a closed n-manifold M is defined as the optimal constant σ(M) satisfying the inequality vol(M, g) ≥ σ(M) sys(M, g) n between the volume and the systole of every metric g on M. First, we show that the systolic volume of connected sums of closed oriented essential manifolds is unbounded. Then, we prove that the systolic volume of every sequence of closed hyperbolic (three-dimensional) manifolds is also unbounded. These results generalize systolic inequalities on surfaces in two different directions. |
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Keywords: | Systole Systolic volume Connected sums Hyperbolic manifolds |
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