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Recently there has been an increased interest in complex dynamics of orientation-reversing maps, in particular in the context of gravitational lensing and as an analogue of reflection groups in Sullivan's dictionary between Kleinian groups and dynamics of (anti-)rational maps. Most of the theory parallels the orientation-preserving case, but there are some intriguing differences. In order to deal with the post-critically finite case, we study anti-Thurston maps (orientation-reversing versions of Thurston maps), and prove an orientation-reversing analogue of Thurston's topological classification of post-critically finite rational maps, as well as the canonical decomposition of obstructed maps, following Pilgrim and Selinger. Using these tools, we obtain a combinatorial classification of critically fixed anti Thurston maps, extending a recently obtained classification of critically fixed anti-rational maps. If time allows, I will explain applications of this classification to gravitational lensing. Based on joint work with Mikhail Hlushchanka.

Classification of Critically Fixed Anti-Thurston Maps 11.3 MB application/pdf

COMD Research Seminar Series: Classification Of Critically Fixed Anti-Thurston Maps