Persistently Foliar Knots in Topology and L-Space Surgery

Watch a 53-minute mathematics lecture exploring the relationship between taut co-orientable foliations and L-space knots, delivered at the Centre International de Rencontres Mathématiques. Dive into the L-space Knot Conjecture, which proposes that knots without reducible or L-space surgeries are persistently foliar. Learn about constructing families of foliations that realize all boundary slopes, with particular focus on cases where knots are far from being fibered. Examine applications of this approach to alternating and Montesinos knots, discovering how those without reducible or L-space surgeries demonstrate persistent foliarity. Explore findings about connected sums of alternating knots, Montesinos knots, and fibered knots, including how composite knots with persistently foliar summands maintain this property. The lecture, presented in collaboration with Charles Delman, features chapter markers, keywords, abstracts, and bibliographies through CIRM's Audiovisual Mathematics Library platform.