On embeddings of 3-manifolds in symplectic 4-manifolds

Dissertation Defense
Wednesday, June 1, 2022 - 12:01pm for 1.5 hours (actually 80 minutes)
Skiles 006 and ONLINE (zoom)
Anubhav Mukherjee – Georgia Institute of Technology – anubhavmaths@gatech.edu
Anubhav Mukherjee

Zoom Link- https://gatech.zoom.us/j/97563537012?pwd=dlBVUVh2ZDNwdDRrajdQcDltMmRaUT09 (Meeting ID: 975 6353 7012 Passcode: 525012)


In this talk I will discuss the conjecture that every 3 manifolds can be smoothly embedded in symplectic 4 manifolds. I will give some motivation on why is this an interesting conjecture. As an evidence for the conjecture, I will prove that every 3 manifolds can be embedded in a topological way and such an embedding can be made a smooth one after a single stabilization. As a corollary of the proof, I will prove that integer/rational cobordism group is generated by Stein fillable 3 manifolds. And if time permits, I will give some idea on how one can try to obstruct smooth embeddings of 3 manifolds in symplectic 4 manifolds.