Distinguishing diffeomorphism types of relative trisections

TL;DR

This paper introduces a capping operation to distinguish diffeomorphism types of relative trisections, providing examples of non-diffeomorphic structures on the same 4-manifold with boundary and analyzing their transformations.

Contribution

It presents a novel capping operation that differentiates relative trisections and explores its effects on the topology of the resulting 4-manifolds.

Findings

Capping operation distinguishes non-diffeomorphic relative trisections.

Examples of different relative trisections on the same 4-manifold.

Analysis of how capping affects the topology of 4-manifolds.

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.