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- W3004411579 abstract "We compare the values of the nonorientable three genus (or, crosscap number) and the nonorientable four genus of torus knots. In particular, let [Formula: see text] be any torus knot with [Formula: see text] even and [Formula: see text] odd. The difference between these two invariants on [Formula: see text] is at least [Formula: see text], where [Formula: see text] and [Formula: see text] and [Formula: see text]. Hence, the difference between the two invariants on torus knots [Formula: see text] grows arbitrarily large for any fixed odd [Formula: see text], as [Formula: see text] ranges over values of a fixed congruence class modulo [Formula: see text]. This contrasts with the orientable setting. Seifert proved that the orientable three genus of the torus knot [Formula: see text] is [Formula: see text], and Kronheimer and Mrowka later proved that the orientable four genus of [Formula: see text] is also this same value." @default.
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- W3004411579 date "2020-03-01" @default.
- W3004411579 modified "2023-09-27" @default.
- W3004411579 title "Comparing nonorientable three genus and nonorientable four genus of torus knots" @default.
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- W3004411579 doi "https://doi.org/10.1142/s0218216520500133" @default.
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