# SFT computations and intersection theory in higher-dimensional contact manifolds

## TL;DR

This paper constructs numerous 5-dimensional contact manifolds with specific tightness and filling properties, introduces new obstruction results for symplectic cobordisms, and applies higher-dimensional intersection theory for holomorphic curves.

## Contribution

It provides the first applications of higher-dimensional Siefring intersection theory in contact and symplectic topology, and constructs new examples of contact manifolds with unique properties.

## Key findings

- Existence of infinitely many non-diffeomorphic tight 5D contact manifolds without strong fillings.
- Obstruction results for symplectic cobordisms independent of polyfold theory.
- Application of higher-dimensional intersection theory to contact topology.

## 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.