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Watch a one-hour mathematics lecture from the Centre International de Rencontres Mathématiques where Professor Tsuboi Takashi explores the group of real-analytic diffeomorphisms, focusing on a key lemma about multiple actions of the standard action on the plane as a final object in circle actions. Learn how this lemma suggests the identity component of real-analytic diffeomorphism groups is perfect, building on previous lectures covering Herman's theorem on n-torus diffeomorphisms and the regimentation lemma. Recorded during the "Foliations and Diffeomorphism Groups" thematic meeting in Marseille, France, this advanced mathematics presentation demonstrates why the group of real-analytic diffeomorphisms remains an intriguing object of study despite its apparent rigidity. Access additional features through CIRM's Audiovisual Mathematics Library including chapter markers, keywords, abstracts, and mathematical classifications for enhanced learning.
