# Workshop on the h-principle and beyond

## Flexibilization as localization

Abstract: 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 & Time

November 05, 2021 | 11:45am – 12:45pm

### Location

Simonyi 101 and Remote Access

Oleg Lazarev

### Speaker Affiliation

University of Massachusetts, Boston