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- W2078504504 abstract "We study cosmetic crossings in knots of genus one and obtain obstructions to such crossings in terms of knot invariants determined by Seifert matrices. In particular, we prove that for genus one knots the Alexander polynomial and the homology of the double cover branching over the knot provide obstructions to cosmetic crossings. As an application we prove the nugatory crossing conjecture for twisted Whitehead doubles of non-cable knots. We also verify the conjecture for several families of pretzel knots and all genus one knots with up to 12 crossings." @default.
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- W2078504504 date "2012-01-01" @default.
- W2078504504 modified "2023-09-30" @default.
- W2078504504 title "Cosmetic crossings and Seifert matrices" @default.
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- W2078504504 doi "https://doi.org/10.4310/cag.2012.v20.n2.a1" @default.
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