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• W3104506578 abstract "For each natural number <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n greater-than-or-equal-to 4> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mn>4</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n geq 4</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we determine the unique lowest volume hyperbolic <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=3> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=application/x-tex>3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>–orbifold whose torsion orders are bounded below by <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=application/x-tex>n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. This lowest volume orbifold has base space the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=3> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=application/x-tex>3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>–sphere and singular locus the figure–<inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=8> <mml:semantics> <mml:mn>8</mml:mn> <mml:annotation encoding=application/x-tex>8</mml:annotation> </mml:semantics> </mml:math> </inline-formula> knot, marked <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=application/x-tex>n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We apply this result to give sharp lower bounds on the volume of a hyperbolic manifold in terms of the order of elements in its symmetry group." @default.
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• W3104506578 date "2017-04-13" @default.
• W3104506578 modified "2023-10-14" @default.
• W3104506578 title "The lowest volume $3$–orbifolds with high torsion" @default.
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• W3104506578 doi "https://doi.org/10.1090/tran/6920" @default.
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