L-spaces and knot traces

Abstract: There has been a great deal of interest in understanding which knots are characterized by which of their Dehn surgeries. We study a 4-dimensional version of this question: which knots are determined by which of their traces? We prove several results that are in stark contrast with what is known about characterizing surgeries, most notably that the 0-trace detects every L-space knot. Our proof combines tools in Heegaard Floer homology with results about surface homeomorphisms and their dynamics.