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- W3129104510 abstract "Abstract We show that the length R of a systole of a closed hyperbolic n -manifold $$(n ge 3)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> admitting a triangulation by t n -simplices can be bounded below by a function of n and t , namely $$begin{aligned} R ge frac{1}{2^{(nt)^{O(n^4t)} }} . end{aligned}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo>≥</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:msup> <mml:mn>2</mml:mn> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>n</mml:mi> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:msup> </mml:msup> </mml:mfrac> <mml:mo>.</mml:mo> </mml:mrow> </mml:mtd> </mml:mtr> </mml:mtable> </mml:mrow> </mml:math> We do this by finding a relation between the number of n -simplices and the diameter of the manifold and by giving explicit bounds for a well known relation between the length of the core curve of a Margulis tube and its radius. We prove the same result for finite volume manifolds, with a similar but slightly more involved proof." @default.
- W3129104510 created "2021-02-15" @default.
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- W3129104510 date "2022-09-19" @default.
- W3129104510 modified "2023-09-26" @default.
- W3129104510 title "Systole length in hyperbolic n-Manifolds" @default.
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- W3129104510 doi "https://doi.org/10.1007/s10711-022-00727-1" @default.
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