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Satellite knots and trivializing bands
Preview AbstractWe show an infinite family of satellite knots that can be unknotted by a single band move, but such that there is no band unknotting the knots which is disjoint from the satellite torus.
The non-orientable 4-genus for knots with 10 crossings
Preview AbstractGiven a knot in the 3-sphere, the non-orientable 4-genus or 4-dimensional crosscap number of a knot is the minimal first Betti number of non-orientable surfaces, smoothly and properly embedded in the 4-ball, with boundary the knot. In this paper, we calculate the non-orientable 4-genus of knots with crossing number 10.