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<p>We show that the manifold <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(X=S^2\times S^3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>X</mi> <mo>=</mo> <msup> <mi>S</mi> <mn>2</mn> </msup> <mo>×</mo> <msup> <mi>S</mi> <mn>3</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> has infinitely many structures of a fiber bundle over the base <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(B=S^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>B</mi> <mo>=</mo> <msup> <mi>S</mi> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>. In fact for every lens space <i>L</i>(<i>p</i>,&#xa0;1) there is a fiber bundle <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L(p,1)\rightarrow X\rightarrow B\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>L</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mi>X</mi> <mo stretchy="false">→</mo> <mi>B</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Manifold with Infinitely Many Fibrations Over the Sphere

  • 期刊论文

  • 发表日期：

    2025年7月23日

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  • Zbigniew Jelonek,
  • Włodzimierz Jelonek

摘要

We show that the manifold \(X=S^2\times S^3\) X = S 2 × S 3 has infinitely many structures of a fiber bundle over the base \(B=S^2\) B = S 2 . In fact for every lens space L(p, 1) there is a fiber bundle \(L(p,1)\rightarrow X\rightarrow B\) L ( p , 1 ) → X → B .