Scholarlink

<p>We develop the theory of nilpotent <i>G</i>-spaces and their localisations, for <i>G</i> a compact Lie group, via reduction to the non-equivariant case using Bousfield localisation. One point of interest in the equivariant setting is that we can choose to localise or complete at different sets of primes at different fixed point spaces—and the theory works out just as well provided that you invert more primes at <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40062_2025_371_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(K \le G\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>≤</mo> <mi>G</mi> </mrow> </math></EquationSource> </InlineEquation> than at <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40062_2025_371_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(H \le G\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mo>≤</mo> <mi>G</mi> </mrow> </math></EquationSource> </InlineEquation>, whenever <i>K</i> is subconjugate to <i>H</i> in <i>G</i>. We also develop the theory in an unbased context, allowing us to extend the theory to <i>G</i>-spaces which are not <i>G</i>-connected.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Localisations and completions of nilpotent G-spaces

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年4月11日

查看全文
  • Andrew Ronan

摘要

We develop the theory of nilpotent G-spaces and their localisations, for G a compact Lie group, via reduction to the non-equivariant case using Bousfield localisation. One point of interest in the equivariant setting is that we can choose to localise or complete at different sets of primes at different fixed point spaces—and the theory works out just as well provided that you invert more primes at \(K \le G\) K ≤ G than at \(H \le G\) H ≤ G , whenever K is subconjugate to H in G. We also develop the theory in an unbased context, allowing us to extend the theory to G-spaces which are not G-connected.