<p>In this note we prove that two seemingly different smooth 4-manifolds arising as quotients of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40062_2025_382_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">\(S^2\times S^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>S</mi> <mn>2</mn> </msup> <mo>×</mo> <msup> <mi>S</mi> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> by free actions of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40062_2025_382_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {Z}/4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">Z</mi> <mo stretchy="false">/</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> are in fact diffeomorphic, answering a question of Hambleton and Hillman.</p>

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On two quotients of \(S^2\times S^2\)

  • Andrea Bianchi

摘要

In this note we prove that two seemingly different smooth 4-manifolds arising as quotients of \(S^2\times S^2\) S 2 × S 2 by free actions of \(\mathbb {Z}/4\) Z / 4 are in fact diffeomorphic, answering a question of Hambleton and Hillman.