The lowest volume 3–orbifolds with high torsion
| Autor: | Christopher K. Atkinson, David Futer |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Applied Mathematics General Mathematics Base space 010102 general mathematics Hyperbolic manifold Geometric Topology (math.GT) 57M50 57M60 57R18 Natural number Symmetry group Mathematics::Geometric Topology 01 natural sciences Mathematics - Geometric Topology Bounded function 0103 physical sciences FOS: Mathematics Torsion (algebra) 010307 mathematical physics 0101 mathematics Orbifold Mathematics |
| Zdroj: | Transactions of the American Mathematical Society. 369:5809-5827 |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/tran/6920 |
| Popis: | For each natural number n >= 4, we determine the unique lowest volume hyperbolic 3-orbifold whose torsion orders are bounded below by n. This lowest volume orbifold has base space the 3-sphere and singular locus the figure-8 knot, marked n. 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. 17 pages, 1 figure. v2 contains minor edits. To appear in Transactions of the AMS |
| Databáze: | OpenAIRE |
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