"This thesis studies the Ozsvath-Stipsicz-Szabo Upsilon-invariant and Rasmussen's 'local h-invariants' of satellite knots. The first main result is an inequality relating the Upsilon-invariant of a knot and that of its cable knots. This result generalizes previous work on the Ozsva-Szabo tau-invariant of cable knots due to Hedden and Van Cott. The second main result is a set of inequalities for the local h-invariants, showing their values of a satellite knot are constrained by those of the companion knot and pattern knot. This result generalizes crossing change inequalities and subadditivity. Both results are applied to study the smooth knot concordance group: we use iterated cabling operations to construct infinite-rank summands consisting of topologically slice knots; for any slice pattern with winding number greater than one, we show iterated satellite operations yield infinite-rank subgroups; we also show for a class of winding-number-one pattern which includes the Mazur pattern, the iterated satellite operations still yield infinite-rank subgroups."--Page ii.
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