Exotic 4-manifolds with small trisection genus

TL;DR

This paper constructs exotic 4-manifolds with boundary having low trisection genus and develops genus-3 relative trisections for an infinite family of contractible 4-manifolds, advancing understanding of 4-manifold topology.

Contribution

It introduces new exotic 4-manifolds with boundary of genus 4 and provides genus-3 relative trisections for a broad class of contractible 4-manifolds, expanding the toolkit for 4-manifold decomposition.

Findings

Existence of exotic pairs with boundary and genus 4 trisection

Genus-3 relative trisections for infinite family of contractible 4-manifolds

Advancement in low-genus trisection constructions

Abstract

We show that there exists an exotic pair of $4$-manifolds with boundary whose trisection genera are $4$. We also construct genus-$3$ relative trisections for an infinite family of contractible $4$-manifolds introduced by Akbulut and Kirby.