Triviality of fibers for Misiurewicz parameters in the exponential family

TL;DR

This paper proves that fibers of postcritically finite parameters in the exponential family are trivial, advancing understanding of the structure of non-escaping parameters in complex dynamics.

Contribution

It establishes the triviality of fibers for Misiurewicz parameters in the exponential family, a fundamental step in understanding parameter space structure.

Findings

Fibers of postcritically finite parameters are trivial.

First results on fiber triviality for non-escaping parameters in exponential maps.

Provides a basis for further exploration of exponential family dynamics.

Abstract

We consider the family of holomorphic maps e^z+c and show that fibers of postcritically finite parameters are trivial. This can be seen as the first and simplest class of non-escaping parameters for which we can obtain results about triviality of fibers in the exponential family.