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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Sabourau, S. Systolic volume of hyperbolic manifolds and connected sums of manifolds. Geom Dedicata 127, 7–18 (2007). https://doi.org/10.1007/s10711-007-9146-8
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DOI: https://doi.org/10.1007/s10711-007-9146-8