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<p>We show the existence of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11784_2025_1179_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="TEX">\(S^1\times C_p\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>S</mi> <mn>1</mn> </msup> <mo>×</mo> <msub> <mi>C</mi> <mi>p</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>-maps between certain representation spheres. As an application, we show that, in the family of abelian compact Lie groups, a group <i>G</i> has the weak Borsuk–Ulam property (in the sense of Bartsch) if and only if <i>G</i> is either a finite abelian <i>p</i>-group or a <i>k</i>-torus.</p>

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The existence of \(S^1\times C_p\)-maps between representation spheres and its applications

  • 期刊论文

  • 发表日期：

    2025年3月13日

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  • Ikumitsu Nagasaki

摘要

We show the existence of \(S^1\times C_p\) S 1 × C p -maps between certain representation spheres. As an application, we show that, in the family of abelian compact Lie groups, a group G has the weak Borsuk–Ulam property (in the sense of Bartsch) if and only if G is either a finite abelian p-group or a k-torus.