Title: Symmetric topological complexity and the embedding dimension of projective spaces

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Abstract: In this talk we extend, to the realm of embeddings, Farber's connection between the immersion dimension of projective spaces and their topological complexity. The latter is a LS-model measuring the continuity instabilities inherent in any motion planning algorithm of a given mechanical system. We show that the symmetrized version of such a concept sharply captures the embedding dimension of real projective spaces.