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<p>In this paper, we prove that the trisection genus of the Akbulut cork is 3 and construct infinitely many corks with trisection genus 3. These results give the first examples of contractible 4-manifolds whose trisection genera are determined except for the 4-ball. We also give a lower bound for the trisection genus of a 4-manifold with boundary. In addition, we construct low genus relative trisection diagrams of an exotic pair of simply-connected 4-manifolds with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10711_2025_987_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(b_2 = 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Minimal genus relative trisections of corks

  • 期刊论文

  • 发表日期：

    2025年3月3日

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  • Natsuya Takahashi

摘要

In this paper, we prove that the trisection genus of the Akbulut cork is 3 and construct infinitely many corks with trisection genus 3. These results give the first examples of contractible 4-manifolds whose trisection genera are determined except for the 4-ball. We also give a lower bound for the trisection genus of a 4-manifold with boundary. In addition, we construct low genus relative trisection diagrams of an exotic pair of simply-connected 4-manifolds with \(b_2 = 1\) b 2 = 1 .