## Topology Seminar (Main Talk): Obstructing pseudo-convex embeddings of Brieskorn spheres into complex 2-space

Seminar | March 8 | 4:10-5 p.m. | 3 Evans Hall

Bulent Tosun, University of Alabama

Department of Mathematics

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. This is a joint work with Tom Mark.

hongbins@berkeley.edu