Non-diffeomorphic minimal genus relative trisections of the same 4-manifold

TL;DR

This paper demonstrates that a single 4-manifold with boundary can have multiple, non-diffeomorphic minimal genus relative trisections of the same type, revealing new complexity in 4-manifold topology.

Contribution

It introduces a simple operation to generate a closed 4-manifold diagram from a relative trisection diagram, showing the existence of non-diffeomorphic minimal genus relative trisections.

Findings

Existence of a 4-manifold with boundary with two non-diffeomorphic minimal genus relative trisections.

A new operation to produce a closed 4-manifold diagram from a relative trisection diagram.

Illustration of complexity in the classification of 4-manifolds with boundary.

Abstract

We show the existence of a $4$-manifold with boundary that admits two non-diffeomorphic minimal genus relative trisections of the same $(g,k;p,b)$-type. To prove this, we introduce a simple operation that produces a trisection diagram of a closed $4$-manifold from a relative trisection diagram.