Danica Kosanovic: Claspers, Graspers, Barbells and Diffeomorphisms of S^1 x S^3

Infinite lists of non-isotopic and independent diffeomorphisms of S^1 x S^3 have been constructed by Budney and Gabai using barbells, and by Watanabe using claspers. In this talk I will explain how barbells can be obtained from families of dancing circles, called graspers. This perspective is powerful in certain settings, where it provides quick proofs of existence of infinite subgroups of mapping class groups.

Recording during the thematic meeting : «Trisections and related topics» the October 16, 2025 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker : Guillaume Hennenfent

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