From Liouville Cobordisms to LCS Manifolds

In dimensions greater than four, the classification of smooth manifolds is an unsolvable problem, but manifolds can still be classified up to cobordism.

From this perspective, Liouville cobordisms provide a powerful tool for studying contact manifolds in high dimensions. In this talk, I will explain how Liouville cobordisms can be used to construct exact locally conformally symplectic (LCS) manifolds, in particular the LCS mapping tori associated with a contactomorphism. I will then use this construction to study the isomorphism classes of LCS mapping tori and explore their connections with the contact mapping class group.