Trace-free characters and abelian knot contact homology II
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arXiv
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| Format: | Preprint |
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2017
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| _version_ | 1866908840000225280 |
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| author | Nagasato, Fumikazu Suzuki, Shinnosuke |
| author_facet | Nagasato, Fumikazu Suzuki, Shinnosuke |
| contents | We show that the $(4,5)$- and $(5,6)$-torus knots admit ghost characters. Consequently, these knots provide counterexamples to Ng's conjecture, which proposes an isomorphism between the complexification of degree $0$ abelian knot contact homology and the coordinate ring of the character variety of the $2$-fold branched cover of the $3$-sphere branched along a knot. While Ng's conjecture has been verified for all $2$-bridge and $3$-bridge knots, we demonstrate, via ghost characters, how this isomorphism fails for these torus knots. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1708_00874 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Trace-free characters and abelian knot contact homology II Nagasato, Fumikazu Suzuki, Shinnosuke Geometric Topology 57K31 (Primary), 57K18 (Secondary) We show that the $(4,5)$- and $(5,6)$-torus knots admit ghost characters. Consequently, these knots provide counterexamples to Ng's conjecture, which proposes an isomorphism between the complexification of degree $0$ abelian knot contact homology and the coordinate ring of the character variety of the $2$-fold branched cover of the $3$-sphere branched along a knot. While Ng's conjecture has been verified for all $2$-bridge and $3$-bridge knots, we demonstrate, via ghost characters, how this isomorphism fails for these torus knots. |
| title | Trace-free characters and abelian knot contact homology II |
| topic | Geometric Topology 57K31 (Primary), 57K18 (Secondary) |
| url | https://arxiv.org/abs/1708.00874 |