Rigidity and symmetry of cylindrical handlebody-knots
| Autor: | Wang, Yi-Sheng |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A recent result of Funayoshi-Koda shows that a handlebody-knot of genus two has a finite symmetry group if and only if it is hyperbolic -- the exterior admits a hyperbolic structure with totally geodesic boundary -- or irreducible, atoroidal, cylindrical -- the exterior contains no essential disks or tori but contains an essential annulus. Based on the Koda-Ozawa classification theorem, essential annuli in an irreducible, atoroidal handlebody-knots of genus two are classified into four classes: type $2$, type $3$-$2$, type $3$-$3$ and type $4$-$1$. We show that under mild condition most genus two cylindrical handlebody-knot exteriors contain no essential disks or tori, and when a type $3$-$3$ annulus exists, it is often unique up to isotopy; a classification result for symmetry groups of such cylindrical handlebody-knots is also obtained. Comment: 34 pages, 35 figures |
| Databáze: | arXiv |
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