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The discriminant and oscillation lengths for contact and Legendrian isotopies

Vincent ColinSheila Sandon — 2015

Journal of the European Mathematical Society

We define an integer-valued non-degenerate bi-invariant metric (the discriminant metric) on the universal cover of the identity component of the contactomorphism group of any contact manifold. This metric has a very simple geometric definition, based on the notion of discriminant points of contactomorphisms. Using generating functions we prove that the discriminant metric is unbounded for the standard contact structures on 2 n × S 1 and P 2 n + 1 . On the other hand we also show by elementary arguments that the...

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