Heegaard Floer homology and L-space knots

Heegaard Floer theory consists of a set of invariants of three- and four-dimensional manifolds. Three-manifolds with the simplest Heegaard Floer invariants are called L-spaces, and the name stems from the fact that lens spaces are L-spaces. The overarching goal of the dissertation is to understand L-spaces better. More specifically, this dissertation could be considered as a step towards finding topological characterizations of L-spaces and L-space knots without referencing Heegaard Floer homology. We study knots in S3 that admit positive L-space Dehn surgeries. In particular, we give new examples of knots in S3 within both the families of hyperbolic and satellite knots admitting L-space surgeries. It should be pointed out that for satellite knot examples, we use Berge-Gabai knots (i.e. knots in S1 times D2 with non-trivial solid torus Dehn surgeries) as the pattern. Moreover, we study the relationship between satellite knots and L-space surgeries in the general setting, i.e. when the pattern is an arbitrary knot in S1 times D 2.