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Flexibility for tangent curves in higher dimension

Universidad Complutense de Madrid

Is it always possible to park a car in a parking space whose size is exactly the same as the car? Can we do the same with a multi-trailer truck? In this talk, we will show the relationship between these two questions and the theory of distributions on differentiable manifolds. We will review this theory and focus our attention on bracket-generating distributions. Typical examples of this class of distributions are Contact and Engel structures. We will motivate these objects by showing other examples and establish several results about their tangent curves. In particular, we will show that the spaces of regular tangent knots are flexible if the dimension of the manifold is greater than $3$. These results are part of a joint work with Álvaro del Pino (Utrecht University).

Seminario 1 (IMAG)

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I Coloquio de Geometría y Topología Granada-Málaga

Universidad de Málaga (España)

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ETH Zürich (Switzerland)

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