Flexibilization as localization

Cieliebak and Eliashberg showed that there is a special class of flexible symplectic structures that satisfy an h-principle and hence  have `trivial' symplectic topology. In this talk, I will explain that it is fruitful to think of flexibilization as a  localization functor of the category of symplectic manifolds. In particular, I will show that for any collection of primes P, there is a `P-flexibilization' functor that cannot satisfy an h-principle but is still localizing (after inverting subcritical handles and stabilizing), with usual flexibilization corresponding to the `prime' 0. This is a symplectic analog of the localization of classical topological spaces studied by Quillen, Sullivan, and others.

This talk is based on joint work with Zachary Sylvan and Hiro Lee Tanaka.