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- W2949062479 abstract "We show that every nonzero integer occurs in the denominator of a boundary slope for infinitely many (1,1)-knots and that infinitely many (1,1)-knots have boundary slopes of arbitrarily small difference. Specifically, we prove that for any integers m, n > 1 with n odd the exterior of the Montesinos knot K(-1/2, m/(2m pm 1), 1/n) in S^3 contains an essential surface with boundary slope r = 2(n-1)^2/n if m is even and 2(n+1)^2/n if m is odd. If n > 4m, we prove that K(-1/2, m/(2m+1), 1/n) also has a boundary slope whose difference with r is (8m-2)/(n^2-4mn+n), which decreases to 0 as n increases. All of these knots are (1,1)-knots." @default.
- W2949062479 created "2019-06-27" @default.
- W2949062479 creator A5071854558 @default.
- W2949062479 date "2013-01-26" @default.
- W2949062479 modified "2023-09-27" @default.
- W2949062479 title "Denominators and Differences of Boundary Slopes for (1,1)-Knots" @default.
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