Knotted holomorphic discs in C^2

TL;DR

This paper presents a method to construct knotted, proper holomorphic embeddings of the unit disc into complex two-dimensional space, C^2, demonstrating complex topological structures within holomorphic embeddings.

Contribution

The paper introduces the first known construction of knotted proper holomorphic embeddings of the unit disc in C^2, expanding understanding of complex embeddings and knot theory.

Findings

Existence of knotted proper holomorphic embeddings in C^2

New techniques for constructing complex knotted structures

Implications for topology and complex geometry

Abstract

We construct knotted proper holomorphic embeddings of the unit disc in C^2.