Lipshitz, RobertGuth, Gary2024-01-092024-01-092024-01-09https://hdl.handle.net/1794/29188We study properties of surfaces embedded in 4-manifolds by way of HeegaardFloer homology. We begin by showing link Floer homology obstructs concordance through ribbon homology cobordisms; this extends the work of Zemke and Daemi-Lidman-Vela–Vick-Wong. In another direction, we consider the effect of satellite operations on concordances. We show that the map induced by a satellite concordance is determined by the pattern and the map induced by the original concordance map. As an application, we produce the first examples of stably exotic behavior in the four-ball, i.e. we produce exotic disks whose exotic behavior persists under many 1-handle stabilizations. As a second application, in joint work with Hayden-Kang-Park, we show that the positive Whitehead doubling pattern is injective on the class of HFK-distinguishable disks in B4: we show that for any disks D,D′ in B4 which are distinguished by their induced maps on HFK, their positive Whitehead doubles are also distinguished. In particular, Wh+(D) and Wh+(D′) are exotic.en-USAll Rights Reserved.topologyElectronic Thesis or Dissertation