Ribbons, Satellites, and Exotic Phenomena in Heegaard Floer Homology
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Date
2024-01-09
Authors
Guth, Gary
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Publisher
University of Oregon
Abstract
We 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.
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topology