SFT computations and intersection theory in higher-dimensional contact manifolds

Abstract

We construct infinitely many non-diffeomorphic examples of $5$-dimensional contact manifolds which are tight, admit no strong fillings, and do not have Giroux torsion. We obtain obstruction results for symplectic cobordisms, for which we give a proof not relying on the polyfold abstract perturbation scheme for SFT. These results are part of the author's PhD thesis, and are the first applications of higher-dimensional Siefring intersection theory for holomorphic curves and hypersurfaces.