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Arc spaces, motivic measure and Lipschitz geometry of real algebraic sets Parusinski, Adam


We investigate connections between Lipschitz geometry of real algebraic varieties and properties of their arc spaces. First we define a real motivic integral which admits a change of variable formula not only for the birational but also for generically one-to-one Nash maps. As a consequence we obtain an inverse mapping theorem which holds for generically arc-analytic maps. Then we characterize in terms of the motivic measure, germs of arc-analytic homeomorphisms between real algebraic varieties which are bi-Lipschitz for the inner metric. (Based on a joint paper with J.-B. Campesato, T. Fukui, and K. Kurdyka.)

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