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.

Date

Speakers

Oleg Lazarev

Affiliation

University of Massachusetts, Boston