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Explore the construction of infinite lists of non-isotopic and independent diffeomorphisms of S^1 x S^3 through this mathematical lecture. Learn how barbells can be obtained from families of dancing circles called graspers, building upon the foundational work of Budney and Gabai using barbells, and Watanabe using claspers. Discover how this grasper perspective provides powerful tools for quickly proving the existence of infinite subgroups of mapping class groups in certain mathematical settings. The presentation demonstrates the connections between these different geometric constructions and their applications in topology and differential geometry. Recorded during the thematic meeting "Trisections and related topics" at the Centre International de Rencontres Mathématiques in Marseille, France, this 59-minute lecture offers insights into advanced topics in geometric topology and mapping class group theory.
