Title:
On embeddings of 3-manifolds in symplectic 4-manifolds
On embeddings of 3-manifolds in symplectic 4-manifolds
Author(s)
Mukherjee, Anubhav
Advisor(s)
Etnyre, John B.
Editor(s)
Collections
Supplementary to
Permanent Link
Abstract
We proposed a conjecture that every 3-manifolds smoothly embedded in some closed symplectic 4-manifolds. This work shows that any closed oriented 3-manifold can be topologically embedded in some simply-connected closed symplectic 4-manifold, and that it can be made a smooth embedding after one stabilization. As a corollary of the proof we show that the homology cobordism group is generated by Stein fillable 3-manifolds. We also find obstructions on smooth embeddings: there exists 3-manifolds which cannot smoothly embed in a way that appropriately respect orientations in any symplectic manifold with weakly convex boundary.
Sponsor
Date Issued
2022-07-13
Extent
Resource Type
Text
Resource Subtype
Dissertation