Some notes on the spectral sequence relative to <inline-formula id="M2">  <math id="mathml_M2" display="inline" overflow="scroll">  <msub>    <mrow class="MJX-TeXAtom-ORD">      <mrow class="MJX-TeXAtom-ORD">        <mover>          <mi>γ</mi>          <mo stretchy="false">~</mo>        </mover>      </mrow>    </mrow>    <mrow class="MJX-TeXAtom-ORD">      <mi>p</mi>      <mo>−</mo>      <mn>1</mn>    </mrow>  </msub>  <msub>    <mrow class="MJX-TeXAtom-ORD">      <mi>h</mi>    </mrow>    <mrow class="MJX-TeXAtom-ORD">      <mn>0</mn>    </mrow>  </msub>  <msubsup>    <mrow class="MJX-TeXAtom-ORD">      <mi>g</mi>    </mrow>    <mrow class="MJX-TeXAtom-ORD">      <mi>n</mi>    </mrow>    <mrow class="MJX-TeXAtom-ORD">    </mrow>  </msubsup></math></inline-formula>

Zikang YANG; Ting GAO; Yuyu WANG

doi:10.19789/j.1004-9398.2025.04.004

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Publishing Language: Chinese | Open Access

Some notes on the spectral sequence relative to ${\tilde{γ}}_{p - 1} h_{0} g_{n}^{}$

Zikang YANG, Ting GAO, Yuyu WANG(

)

College of Mathematical Science, Tianjin Normal University, Tianjin 300387

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Abstract

Detecting the homotopy group of sphere spectrum is an important problem in homotopy theory and the May spectral sequence is the main tool. In the May spectral sequence, some conclusions of the permanent cycles which can be represented by ${\tilde{γ}}_{p - 1} h_{0} g_{n}$ in the Adams spectral sequence are given with the method of linear algebra, where $p \geq 7$ , $n \geq 4$ .

Keywords

May spectral sequence Ext group Adams spectral sequence

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Journal of Capital Normal University (Natural Science Edition)

Volume 46 Issue 4,
August 2025

Pages 32-36

DOI: 10.19789/j.1004-9398.2025.04.004

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Cite this article:

YANG Z, GAO T, WANG Y. Some notes on the spectral sequence relative to

{\tilde{γ}}_{p - 1} h_{0} g_{n}^{}

. Journal of Capital Normal University (Natural Science Edition), 2025, 46(4): 32-36. https://doi.org/10.19789/j.1004-9398.2025.04.004

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Received: 13 April 2023

Published: 01 August 2025

This is an open access article under the CC BY-NC-ND 4.0 license (https://creativecommons.org/licenses/by-nc-nd/4.0/).

Some notes on the spectral sequence relative to γ ~ p − 1 h 0 g n

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Some notes on the spectral sequence relative to ${\tilde{γ}}_{p - 1} h_{0} g_{n}^{}$