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<p>We prove that if a closed manifold <i>B</i> is a connected component of the binding of an open book decomposition of a manifold <i>M</i>, then every open book decomposition of <i>B</i> spun embeds in <i>M</i>. As an application, we prove that every open book decomposition of a simply connected spin 5-manifold spun embeds in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {S}^7\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">S</mi> </mrow> <mn>7</mn> </msup> </math></EquationSource> </InlineEquation> and every 3-dimensional open book spun embeds in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {S}^5\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">S</mi> </mrow> <mn>5</mn> </msup> </math></EquationSource> </InlineEquation>. We also define a notion of spun embedding for Morse open books.</p>

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A note on codimension 2 spun embedding

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Sneha Banerjee,
  • Shital Lawande,
  • Subhadeep Rana,
  • Kuldeep Saha

摘要

We prove that if a closed manifold B is a connected component of the binding of an open book decomposition of a manifold M, then every open book decomposition of B spun embeds in M. As an application, we prove that every open book decomposition of a simply connected spin 5-manifold spun embeds in \(\mathbb {S}^7\) S 7 and every 3-dimensional open book spun embeds in \(\mathbb {S}^5\) S 5 . We also define a notion of spun embedding for Morse open books.