Homotopy invisibility of Singular Curves

Francesco Boarotto
Wednesday, November 25, 2015 - 14:00

In this talk we are going to show that for the generic sub-Riemannian structure we can perform an analogue of the classical Morse theory. In particular we will show that if there are no critical points of the extended endpoint map between two sublevel of the energy E_1<E_2 and eps>0 is a small parmeter, it is possible to deform any compact set in the space of controls having energy not greater than E_2 to a compact set having energy not greater than E_1+eps. As a corollary, we will provide the counterpart of the classical min-max theorem for normal geodesics. If time permits we will discuss consequences and open problems related to our contruction.

This is a joint work with A. Lerario and A. A. Agrachev.

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