On the dynamical Teichm\"uller space
Matthieu Astorg (IMT)
TL;DR
This paper demonstrates that the dynamical Teichmüller space of a rational map can be embedded into the space of rational maps of the same degree, providing new insights into its structure.
Contribution
It introduces a novel description of the tangent and cotangent spaces to the dynamical Teichmüller space, answering a question posed by McMullen and Sullivan.
Findings
Dynamical Teichmüller space immerses into rational maps space
New description of tangent and cotangent spaces
Addresses a question by McMullen and Sullivan
Abstract
We prove that the dynamical Teichm\"uller space of a rational map immerses into the space of rational maps of the same degree, answering a question of McMullen and Sullivan. This is achieved through a new description of the tangent and cotangent space to the dynamical Teichm\"uller space.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometry and complex manifolds · Geometric and Algebraic Topology