1
$\begingroup$

Suppose we have a contact manifold (M,$\xi$) and two associated contact forms $\alpha$ and $\beta$ s.t.$\beta=f\alpha$ with $f>0$. Suppose also that we have two almost complex structures $J_\alpha$ and $J_\beta$ on $\xi$ compatible with/tamed by $d\alpha$ and $d\beta$ respectively. Is it possible to define a symplectic cobordism $\mathbb{R}\times M$ (with a cylindrical almost complex structure) such that above the level $b$, we have the data associated to $\beta$ and below the level $a$, we have the data associated to $\alpha$ for some $b>a$ and such that for any holomorphic cylinder, we have the upper action $\geq$ the lower action?

Thanks for your interest.

$\endgroup$

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.