Exceptional Seifert fibered surgeries on Montesinos knots and distinguishing smoothly and topologically doubly slice knots
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The results presented in this thesis pertain to two distinct areas of low-dimensional topology. First, we give a classification of small Seifert fibered surgeries on hyperbolic pretzel knots, as well as a near-classification of small Seifert fibered surgeries on hyperbolic Montesinos knots. Along with recent results of Ichihara-Masai [IM13], these results complete the classification of all exceptional Dehn surgeries on arborescent knots. Second, we exhibit an infinite family of smoothly slice knots that are topologically doubly slice, but not smoothly doubly slice. A subfamily of these knots is then used to show that the subgroup of the smooth double concordance group consisting of topologically doubly slice knots is infinitely generated. One corollary of these results is that there exist infinitely many rational homology 3-spheres (with nontrivial first homology) that embed topologically, but not smoothly, into the 4-sphere.