Toda-Smith谱同伦群的具有第六滤子的新非平凡元素族

当p≥7,n ≥ 3时,本文找到一个永久循环(φhn)″=φ"*(hn)′∈Ext2,pnq+2q-1A(H*L∧K,H*K),它在Adams谱序列中收敛到[∑pnq+2q-3K,L∧K]的一个非零元素,由Adams分解得到η"n,2∈[∑pnq+2q-1K,E2∧L∧K],使得(b2∧1L∧K)η"n,2=(φhn)″,进而得到f∈[∑pnq+(3p2+3p+4)q-5S,K]并且它具有第六滤子.     

Adams谱序列中的两个非平凡微分

令p≥5为奇素数,研究Adams谱序列的二阶微分d2:Ext*0.     

Moore谱的Adams谱序列中的一个非平凡微分

令p是一个大于5的奇素数．本文证明了在收敛到Moore谱的稳定同伦群的Adams谱序列中,在相差一个非零系数下,h_2的2p阶Adams微分是a_1b_0~p．     

球面稳定同伦群的一族新元素(γ)th0b41

证明了在Adams谱序列中存在永久循环元hob41,且可收敛到稳定同伦群π其中V(n)是Toda-Smith谱.进而,利用Yoneda乘积,证明了在Adams谱序列中还存在永久循环元(γ)th0b41收敛到球面稳定同伦群π*(S)的一个非零元.     

ON AN INFINITE FAMILY IN π_S*

In this paper, a new family of homotopy elements in the stable homotopy groups of spheres represented by h1 hn hm γs in the Adams spectral sequence is detected, where n- 2 ≥ m ≥ 5 and 3 ≤ s p.     

古典Adams谱序列中的一个非平凡乘积元

证明了古典Adams谱序列中的乘积元b_0~2β_s∈Ext_A~(s+4,t(s))(Z_p,Z_p)的非平凡性,其中p≥11,2≤sp-2,t(s)=2(p-1)[(s+2)p+(s-1)]+(s-2).     

On the Convergence of Products γ^-sh1hn in the Adams Spectral Sequence

Abstract Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by （b0hn-h1bn-1）∈ ExtA^3,（p^n＋p）q（Zp,Zp） in the Adams spectral sequence. At the same time, he proved that i.（hlhn） ∈ExtA^2,（p^n＋P）q（H^＊M, Zp） is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element ξn∈π（p^n＋p）q-2M. In this paper, with Lin＇s results, we make use of the Adams spectral sequence and the May spectral sequence to detect a new nontrivial family of homotopy elements jj′j^-γsi^-i′ξn in the stable homotopy groups of spheres. The new one is of degree p^nq ＋ sp^2q ＋ spq ＋ （s - 2）q ＋ s - 6 and is represented up to a nonzero scalar by hlhnγ-s in the E2^s＋2,＊-term of the Adams spectral sequence, where p ≥ 7, q = 2（p - 1）, n ≥ 4 and 3 ≤ s 〈 p.     

A NEW FAMILY OF FILTRATION s＋6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

In the year 2002, Lin detected a nontrivial family in the stable homotopy groups of spheres πt-6S which is represented by hngor3 ∈ ExtA6,t(Zp,Zp) in the Adams spectral sequence, where t=2pn(p-1) 6(p2 p 1)(p-1) and p≥7 is a prime number.This article generalizes the result and proves the existence of a new nontrivial family of filtration s 6 in the stable homotopy groups of spheres πt1-s-6S which is represented by hngors 3 6 ExtAs 6,t1(Zp, Zp) in the Adams spectral sequence, where n≥4, 0≤s相似文献   

May谱序列的一些注记

令 p>5 是素数, A 表示模 p Steenrod代数, S 表示球谱的 p 局部化. 首先给出了有关May谱序列的一些重要定理, 然后作为应用, 利用May谱序列和Adams谱序列发觉了一族新的非零的球面稳定元素. 该新元素族次数为2(p-1)(pⁿ+sp²+sp+s)-7,在Adams谱序列中由 b_n-1g0γ_s∈ Ext_A^s+4,﹡( Z_pZ_p)所表示, 其中n≥4, 3≤s

     

球面稳定同伦群的γ_tl_1g_0新元素族

首先给出了May谱序列E_1~(s,t,u)项的几个结果,然后利用这些结果和关于Ext_P~(s,t)(Z_p,Z_p)的一个估计(P为由mod p Steenrod代数A的所有循环缩减幂P~i(i≥0)生成的子代数)得出了乘积(?)t (?)g0∈Ext_A~(*,*)(Z_p,Z_p)(3≤t相似文献   

球面稳定同伦群中的一族新元素

本文研究了球面稳定同伦群中元素的非平凡性.利用May谱序列,证明了在Adams谱序列E₂项中存在乘积元素收敛到球面稳定同伦群的一族阶为p的非零元,此非零元具有更高维数的滤子.     

球面稳定同伦中同伦元素β2γs的非平凡性

本文研究了球面稳定同伦中同伦元素β2γs的非平凡性.利用May谱序列和Adams谱序列证明:同伦元素β2γs在一定条件下是阶为p的非平凡元素,其中p≥7是奇素数.     

A NON-TRIVIAL PRODUCT OF FILTRATION s＋6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

By a method improving that of [1], the authors prove the existence of a non-trivial product of filtration, s ＋ 6, in the stable homotopy groups of sphere, πt-6S, which is represented up to non-zero scalar by β^-s＋2ho（hmbn-1 -hnbm-1） ∈ ExtA^s＋6,t＋s（Zp, Zp） in the Adams spectral sequence, where p ≥ 7, n ≥ m ＋ 2 ≥ 5, q = 2（p- 1）, 0 ≤ s 〈 p - 2, t= （s ＋ 2 ＋ （s ＋ 2）p ＋ p^m ＋ p^n）q. The advantage of this method is to extend the range of s without much complicated argument as in [1].     

SOME NEW FAMILIES OF FILTRATION FIVE IN THE STABLE HOMOTOPY OF SPHERES

This study proves a general result on convergence of α2x ∈ ExtA^s＋2.tq＋2q＋1 （Zp, Zp） in the Adams spectral sequence and as a consequence, the study detects some new families in the stable homotopy groups of spheres πtq＋2q-4S which is represented in the Adams spectral sequence by α2fn,α2fn,α2huhmhn ∈ ExtA^5,tq＋2q＋1（Zp,Zp） with tq=p^n＋1q＋2p^nq,2p^n＋1q_P^nq,p^uq＋p^mq＋p^nq,respectively, where α2∈Extα^2,2q＋1（Zp,Zp）,fn∈ExtA^3,p^n＋1q＋2p^nq（Zp,Zp）,fn∈ExtA^3,2p^n＋2q＋p^nq（Zp,Zp）,hn∈ExtA^1,p^nq（Zp,Zp）and p≥5 is a prime,q=2（p=-1）,n≥2.     

球面稳定同伦群的回访新元素族

本文构造了在Adams谱序列中由hng0γ3∈E26,t所表示的球面稳定同伦群πt-6S的新元素族,回访了文[1]中构造的bn-1g0γ3-元素族∈πt-7S,其中t=2pn(p-1)+6(p2+P+1)(p-1),P≥7是素数, n≥4.     

SOME NEW FAMILIES OF FILTRATION FOUR IN THE STABLE HOMOTOPY OF SPHERES

1.IntroductionLetAbethemodSteenrodalgebraandSthespherespectrumlocalizedatanoddprime.TodeterminethestablehomotopygroupsofspheresisoneofthecentralprobleminhomotopytheoryOneofthemaintoolstoreachitistheAdamsspectralsequence(ASS)wherethe-termisthecohomolo...     

Stiff微分方程初值问题的一类数值方法

1.引言 实践表明,数值积分常微分方程初值问题 dx/dt=f(t,x), (1.1) x(t_0)=x_0时,若(1.1)是Stiff的,积分过程的稳定性是一个突出的问题.用传统的数值方法,比如Euler法,Adams法或Runge-Kutta法,为了保证计算稳定,积分步长受到相当地限制.即使运算速度为 100万次/秒的计算机,计算时间也将成为重大的负担.     

具有大稳定域的线性多步方法

§1.引言 解常微分方程初值问题:的线性k步方法为 sum from j=0 to k (α_jy_(n j)=h sum from j=0 to k (β_jf_(n j),(2)其中α_0~2 β_0~2≠0,α_k≠0.当β_k≠0时,(2)为隐式k步法;当β_k=0时,(2)为显式k步法. 若将(2)应用于单个方程 y′=λy,Reλ<0,则得差分方程 ρ(E)y_n=μσ(E)y_(?),μ=λh,     

Sobolev-Lorentz范数约束下的次临界型Adams不等式

本文在Sobolev-Lorentz空间W²L^2,q(R⁴)的范数约束下得到了一个最佳的二阶次临界型Adams不等式.进一步,当次临界指标逼近最佳常数时,得到了Adams泛函的上、下界的估计.本文主要采用了Lam和Lu[A new approach to sharp MoserTrudinger and Adams type inequalities:a rearrangement-free argument,J.Diff Equ.,2013,255(3):298-325]的分割水平集方法.