Obstructing Sliceness in a Family of Montesinos Knots
نویسنده
چکیده
Using Gauge theoretical techniques employed by Lisca for 2-bridge knots and by Greene-Jabuka for 3-stranded pretzel knots, we show that no member of the family of Montesinos knots M(0; [m1 + 1, n1 + 2], [m2 + 1, n2 + 2], q), with certain restrictions on mi, ni, and q, can be (smoothly) slice. Our techniques use Donaldson’s diagonalization theorem and the fact that the 2-fold covers of Montisinos knots bound plumbing 4-manifolds, many of which are negative definite. Some of our examples include knots with signature 0 and square determinant.
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