The Hofer norm of a contactomorphism

@inproceedings{Shelukhin2014TheHN,
  title={The Hofer norm of a contactomorphism},
  author={Egor Shelukhin},
  year={2014}
}
  • Egor Shelukhin
  • Published 2014
  • Mathematics
  • We show that the $L^{\infty}$-norm of the contact Hamiltonian induces a non-degenerate right-invariant metric on the group of contactomorphisms of any closed contact manifold. This contact Hofer metric is not left-invariant, but rather depends naturally on the choice of a contact form $\alpha,$ whence its restriction to the subgroup of $\alpha$-strict contactomorphisms is bi-invariant. The non-degeneracy of this metric follows from an analogue of the energy-capacity inequality. We show… CONTINUE READING

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