<p>We compute the upper characteristic rank of the projective Stiefel manifolds over <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40879_2025_857_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathbb R, \mathbb C$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">R</mi> <mo>,</mo> <mi mathvariant="double-struck">C</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40879_2025_857_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathbb H$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">H</mi> </math></EquationSource> </InlineEquation> and the flip Stiefel manifolds. We also provide bounds for the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40879_2025_857_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">$\textrm{cup}$</EquationSource> <EquationSource Format="MATHML"><math> <mtext>cup</mtext> </math></EquationSource> </InlineEquation> lengths of these spaces as well as necessary conditions for the existence of an <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40879_2025_857_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$S^3$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>S</mi> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>-map between quaternionic Stiefel manifolds using the Fadell–Husseini index.</p>

Some observations on projective Stiefel manifolds

期刊论文
发表日期：

2025年9月10日

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Bikramjit Kundu,
Sudeep Podder

摘要

We compute the upper characteristic rank of the projective Stiefel manifolds over $\mathbb R, \mathbb C$ $R, C$ and $\mathbb H$ $H$ and the flip Stiefel manifolds. We also provide bounds for the $\textrm{cup}$ $cup$ lengths of these spaces as well as necessary conditions for the existence of an $S^3$ $S^{3}$ -map between quaternionic Stiefel manifolds using the Fadell–Husseini index.