For exotic surfaces with boundary, one stabilization is not enough
Year: 2024
Type: article
Abstract: Works of Hosokawa–Kawauchi (1979) and Baykur–Sunukjian (2016) show that homologous surfaces in a 4-manifold become isotopic after a finite number of internal stabilizations, i.e., attaching tubes to the surfaces. A natural question is how many stabilizations are needed before the surfaces become isotopic. In particular, given an exotic pair of surfaces, is a single stabilization always enough to make the pair smoothly isotopic? We answer this question by studying how the stabilization distance between surfaces with boundary changes with respect to satellite operations. Using a range of Floer theoretic techniques, we show that there are exotic disks in the 4-ball which have arbitrarily large stabilization distance, giving the first examples of exotic behavior in the 4-ball for which “one is not enough”.
DOI: 10.4171/jems/1541
Author: Gary Guth
Institution: Stanford University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404611606