Séminaire de topologie, géométrie et algèbre

In a pioneering work from 1998, Eliashberg and Thurston proved that, in ambient dimension $3$, $C^2$ foliations can always (besides one example) be $C^0$-approximated by contact structures in the space of plane fields. To do so, they introduce what they called “confoliations”; these are geometric structures which are mid-way between foliations and contact structures. While these have been studied extensively in dimension $3$, the situation in higher dimensions is less clear, and there is not even a consensus on what their definition should be. In this talk, based on joint works with Robert Cardona and with Seungook Yu, I will present a candidate notion of ``high-dimensional (c-)symplectic confoliation'', and explain why it is well suited to generalize some of the 3-dimensional results by Eliashberg and Thurston. I will focus in particular on a Reeb stability type statement, and an obstruction to contact approximations.