A note on the volume flux of smooth and continuous strictly contact isotopies

Details A note on the volume flux of smooth and continuous strictly contact isotopies A note on the volume flux of smooth and continuous strictly contact isotopies

2011-07-25

arxiv.org/abs/1107.4869v1

Mathematics

Symplectic Geometry

8 pages

Scientific paper

This note on the flux homomorphism for strictly contact isotopies complements the recent paper [MS11a] by P. Spaeth and the author. We determine the volume flux restricted to symplectic and volume-preserving contact isotopies and their C^0-limits for some classes of symplectic and contact manifolds and for a number of examples. In particular, we see that the restriction of the flux may fail to be surjective. It vanishes for an isotopy preserving a regular contact form, but can be nontrivial for non-regular contact forms. Applications are discussed in the article cited above. We also find obstructions to regularizing a strictly contact isotopy that are not present for Hamiltonian isotopies [Pol01, Section 5.2] or contact isotopies [MS11b].

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