Distinguishing diffeomorphism types of relative trisections

Abstract

We distinguish diffeomorphism types of relative trisections using a ``capping'' operation, which yields a trisection diagram of a closed 4-manifold from a relative trisection diagram. Using this operation, we give various examples of non-diffeomorphic relative trisections of the same 4-manifold with boundary. We also study how the corresponding trisected 4-manifold changes under the capping operation.