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Explore a groundbreaking lecture that challenges a long-standing conjecture in algebraic topology. Delve into the world of Vietoris-Rips complexes and their connectivity as Žiga Virk presents a counter-example to Hausmann's conjecture from 1995. Learn about the stability property of persistent homology and its crucial role in disproving the monotonicity of Vietoris-Rips complex connectivity. Gain insights into the implications of this discovery for closed compact Riemannian manifolds and their homotopy equivalence to Vietoris-Rips complexes at small scale parameters.
