JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (2): 78-84.doi: 10.6040/j.issn.1671-9352.0.2023.155

Previous Articles    

A note on the basis in cohomology H1,*(A)

QI Xin1, MENG Rui2, WANG Yuyu1*   

  1. 1. College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China;
    2. School of Mathematical Sciences, East China Normal University, Shanghai 200241, China
  • Published:2025-02-14

PDF (PC)

4

Abstract: The non-triviality of the product element h1hn(~overδ)p∈Hp+2,t(A)is proved by using May spectral sequence and the analysis of degree and differential, where n≥6, the odd prime p≥11, t=q［pn+p4+(p-1)p2+(p-1)p+(p-3)］+p-4, q=2(p-1).

Key words: Adams spectral sequence, May spectral sequence, cohomology, May differential, non-triviality

CLC Number: 

  • O189.23
[1] ADAMS J F. Stable homotopy and generalised homotogy[M]. Chicago: University of Chicago Press, 1974.
[2] LIULEVICIUS A. The factorizations of cyclic reduced powers by secondary cohomology operations[J]. Proceedings of the National Academy of Sciences, 1960, 46(7):978-981.
[3] WANG Xiangjun, ZHENG Qibing. The convergence of (~overα)nsh0hk[J]. Science China Mathematics, 1998, 41(6):622-628.
[4] ZHAO Hao, LIU Xiugui, JIN Yinglong. A non-trivial product of filitration s+6 in the stable homotopy groups of spheres[J]. Acta Mathmatica Scientia, 2009, 29(2):276-284.
[5] WANG Yuyu, WANG Jianbo. On a new nontrivial element involving the third periodicity γ-family in π*(S)[J]. Journal of Mathematics, 2017, 37(5):898-910.
[6] 王玉玉, 刘艳芳. 球面稳定同伦群中非平凡元素γsξn[J]. 数学学报(中文版), 2018, 61(6):911-924. WANG Yuyu, LIU Yanfang. The nontrivial element γsξn in the stable homotopy groups of spheres[J]. Acta Mathematica Sinica(Chinese Series), 2018, 61(6):911-924.
[7] GU Xing, WANG Xiangjun, WU Jianqiu. The composition of R. Cohens elements and the third periodic elements in stable homotopy groups of spheres[J]. Osaka Journal of Mathematics, 2021, 58(2):367-382.
[8] LIN Jinkun. Third periodicity families in the stable homotopy of spheres[J]. Journal of Geometry and Topology, 2003, 3(3):179-219.
[9] RAVENEL D C. Complex cobordism and stable homotopy groups of spheres[M]. 2nd ed. NewYork: American Mathematical Society Chelsea Publishing, 2004:347.
[10] ZHONG Linan, WANG Yuyu. Detection of a nontrivial product in the stable homotopy groups of spheres[J]. Algebraic & Geometric Topology, 2013, 13(5):3009-3029.
[11] LIN Jinkun. Some new families of filtration five in the stable homotopy of spheres[J]. Acta Mathematica Scientia, 2009, 29(5):1395-1404.
[1] Wen TENG,Fengshan LONG. Cohomology and deformation of differential Lie-Yamaguti superalgebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(2): 32-37,46.
[2] LIU Yan-ping. Relative derived category with respect to a duality pair [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 23-30.
[3] DING Ya-zhou, WANG Shu-juan. First cohomology of W(2)with coefficients in Kac modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(12): 71-74.
[4] TAN Ling-ling, HUANG Yun-tao, ZHAO Ti-wei. Tate cohomology over T2-extension algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(1): 1-9.
[5] LIU Yan-fang, WANG Yu-yu. Some notes on E2-term of Adams spectral sequence [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(8): 43-48.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd