Winding Numbers And Full Extendibility in Holomorphic Motions

TL;DR

This paper presents a counterexample in holomorphic motions showing that satisfying the zero winding number condition does not guarantee full extendibility.

Contribution

The authors construct a specific example of a holomorphic motion that meets the zero winding number condition but cannot be fully extended, highlighting a limitation in existing theory.

Findings

Counterexample of a holomorphic motion with zero winding number that is not fully extendable

Demonstrates that zero winding number condition alone is insufficient for full extendibility

Provides insight into the structure of holomorphic motions and their extendability constraints

Abstract

We construct an example of a holomorphic motion of a five-point subset of the Riemann sphere over an annulus such that it satisfies the zero winding number condition but is not fully extendable.