Stein fillings vs. Milnor fibers
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915236171218944 |
|---|---|
| author | Baykur, R. Inanc Nemethi, A. Plamenevskaya, O. |
| author_facet | Baykur, R. Inanc Nemethi, A. Plamenevskaya, O. |
| contents | 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 (that is, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12216 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stein fillings vs. Milnor fibers Baykur, R. Inanc Nemethi, A. Plamenevskaya, O. Geometric Topology Algebraic Geometry Symplectic Geometry 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 (that is, 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. |
| title | Stein fillings vs. Milnor fibers |
| topic | Geometric Topology Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2403.12216 |