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- W4288086306 abstract "We extend Culler and Shalen's construction of detecting essential surfaces in 3-manifolds to 3-orbifolds. We do so in the setting of the $mathrm{SL}_2(mathbb{C})$ character variety, and following Boyer and Zhang in the $mathrm{PSL}_2(mathbb{C})$ character variety as well. We show that any slope detected on a canonical component of the $mathrm{(P)SL}_2(mathbb{C})$ character variety of a one cusped hyperbolic 3-manifold with symmetries must be the slope of a symmetric surface. As an application, we show that for each symmetric double twist knot there are slopes which are strongly detected on the character variety but not on the canonical component." @default.
- W4288086306 created "2022-07-28" @default.
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- W4288086306 date "2019-11-01" @default.
- W4288086306 modified "2023-10-18" @default.
- W4288086306 title "Symmetries and Detection of Surfaces by the Character Variety" @default.
- W4288086306 doi "https://doi.org/10.48550/arxiv.1911.00415" @default.
- W4288086306 hasPublicationYear "2019" @default.
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