Obstructing pseudo-convex embeddings of Brieskorn spheres into complex 2-space

Geometry Topology Seminar
Monday, October 24, 2016 - 14:00
1 hour (actually 50 minutes)
Skiles 006
University of Alabama
A Stein manifold is a complex manifold with particularly nice convexity properties. In real dimensions above 4, existence of a Stein structure is essentially a homotopical question, but for 4-manifolds the situation is more subtle.  An important question that has been circulating among contact and symplectic topologist for some time asks: whether every contractible smooth 4-manifold admits a Stein structure? In this talk we will provide examples that answer this question negatively. Moreover, along the way we will provide new evidence to a closely related conjecture of Gompf,  which asserts that a nontrivial Brieskorn homology sphere, with either orientation, cannot be embedded in complex 2-space as the boundary of a Stein submanifold.