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

Publication date: 25 July 2011

Abstract: 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].

Mathematics Subject Classification ID

Global theory of symplectic and contact manifolds (53D35)

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