Thoman Mark -- Symplectic convexity and embeddings of 3-manifolds in 4-space
Author information
- Thoman Mark
- University of Virginia
Abstract:
Every closed oriented 3-dimensional manifold embeds in \(\mathbb R^5\), but it is far from understood which admit embeddings in \(\mathbb R^4\). We will describe two geometric conditions, strict pseudoconvexity and symplectic convexity, that one may impose in order to make progress, and give evidence that symplectic convexity is the stronger constraint. In particular, we will show that among Brieskorn homology spheres, while many admit smooth embeddings in \(\mathbb R^4\), none can be symplectically convex.