Topological regluing of rational functions
Vladlen Timorin

TL;DR
This paper explores the topological operation of regluing in rational functions, providing a framework that connects topological models with holomorphic interpretations, inspired by Thurston–Teichmüller theory.
Contribution
It develops a topological theory of regluing for rational functions and suggests directions for a holomorphic extension of this theory.
Findings
Topological models for rational functions are constructed via regluing.
A connection between regluing and Thurston–Teichmüller theory is established.
Potential for a holomorphic theory of regluing is outlined.
Abstract
Regluing is a topological operation that helps to construct topological models for rational functions on the boundaries of certain hyperbolic components. It also has a holomorphic interpretation, with the flavor of infinite dimensional Thurston--Teichm\"uller theory. We will discuss a topological theory of regluing, and trace a direction in which a holomorphic theory can develop.
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