CR regular embeddings and immersions of compact orientable 4-manifolds into C3

TL;DR

This paper characterizes when compact orientable 4-manifolds can be CR regularly immersed or embedded into complex 3-space, linking these possibilities to specific topological invariants.

Contribution

It provides necessary and sufficient topological conditions for CR regular immersions and embeddings of 4-manifolds into C3, connecting differential topology with CR geometry.

Findings

CR regular immersion exists iff first Pontryagin class and Euler characteristic vanish

CR regular embedding exists iff additionally the second Stiefel-Whitney class vanishes

Topological invariants determine CR embedding and immersion possibilities

Abstract

We show that a compact orientable 4-manifold M has a CR regular immersion into C3 if and only if both its first Pontryagin class and its Euler characteristic vanish, and has a CR regular embedding into C3 if and only if in addition the second Stiefel-Whitney class of M vanishes.