Stein fillings vs. Milnor fibers
Abstract
Abstract Given a link of a normal surface singularity with its canonical contact structure, we compare the collection of its Stein fillings to its Milnor fillings (i.e. Milnor fibers of possible smoothings). We prove that, unlike Stein fillings, Milnor fillings of a given link have bounded topology; for links of sandwiched singularities, we further establish that there are only finitely many Milnor fillings. We discuss some other obstructions for a Stein filling to be represented by a Milnor fiber, and for various types of singularities, including simple classes like cusps and triangle singularities, we produce Stein fillings that do not come from Milnor fibers or resolutions.
Fields of Study & Subjects
Neurofibromatosis and Schwannoma Cases
Geometric and Algebraic Topology
Salivary Gland Tumors Diagnosis and Treatment
Publication details
- Journal / source
- Compositio Mathematica
- Publisher
- Cambridge University Press (CUP)
- Volume
- 162
- Issue
- 7
- Pages
- 1574–1606
- Publication date
- 1 July 2026
- Language
- EN