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- W3099570516 abstract "Let $Ksubset S^3$ be a Fox $p$-colored knot and assume $K$ bounds a locally flat surface $Ssubset B^4$ over which the given $p$-coloring extends. This coloring of $S$ induces a dihedral branched cover $Xto S^4$. Its branching set is a closed surface embedded in $S^4$ locally flatly away from one singularity whose link is $K$. When $S$ is homotopy ribbon and $X$ a definite four-manifold, a condition relating the signature of $X$ and the Murasugi signature of $K$ guarantees that $S$ in fact realizes the four-genus of $K$. We exhibit an infinite family of knots $K_m$ with this property, each with a {Fox 3-}colored surface of minimal genus $m$. As a consequence, we classify the signatures of manifolds $X$ which arise as dihedral covers of $S^4$ in the above sense." @default.
- W3099570516 created "2020-11-23" @default.
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- W3099570516 date "2020-07-20" @default.
- W3099570516 modified "2023-09-25" @default.
- W3099570516 title "The dihedral genus of a knot" @default.
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- W3099570516 doi "https://doi.org/10.2140/agt.2020.20.1939" @default.
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