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同伦群
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  homotopy group
     Two New Elements of the Stable Homotopy Group of Spheres h_0(b_1)~3γ_3 and (b_1)~3g_0γ_3
     球面稳定同伦群的两个新元素h_0(b_1)~3γ_3和(b_1)~3g_0γ_3
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     A New Family Elements in the Stable Homotopy Group G_0(B_1)~4■_s
     球面稳定同伦群的一族新元素G_0(B_1)~4■_s
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     A New Family Elements in the Stable Homotopy Group g_0(b_1)~2■_s
     球面稳定同伦群的一族新元素g_0(b_1)~2■_s
短句来源
     TWO NEW ELEMENTS OF THE STABLE HOMOTOPY GROUP OF SPHERES: h_0(b_1)~3■_s AND (b_1)~3g_0■_s
     球面稳定同伦群的两个新元素h_0(b_1)~3_s)和(b_1)~3g_0_s)
短句来源
     When X is sphere spectrum S, Moore spectum M, Toda-Smith spectrum V(1) respectively, (πt-sX)p is respectively the stable homotopy group of S, M, V(1).
     当X是球谱S, Moore谱M,Toda-Smith谱V(1)时,(πt-sX)p分别为S,M,v(1)的稳定同伦群.
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  homotopy groups
     In this paper, it is proved that for p≥7 an arbitrary odd prime number and 3≤s< p, the homotopy elementα1β1γs is nontrivial and of order p in the stable homotopy groups of spheresπ*S.
     本文证明:当p≥7任意奇素数,3≤s同伦群π*S中的一个阶为p的非平凡元素.
短句来源
     A NEW FAMILY REPRESENTED BY b_1g_0(γ|-)_s IN THE STABLE HOMOTOPY GROUPS OF SPHERES
     球面稳定同伦群中的一个新元素族b_1g_0(γ|~)_s
短句来源
     PSEUDOMANIFOLD AND MANIFOLD HOMOTOPY GROUPS
     假流形同伦群与流形同伦群(英文)
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     This paper detects a new family nonzero elements γth0b21 of the stable homotopy groups of sphere and a nonzero element h0b21 of Toda-Smith spectrum V(1) by using of the ASS.
     本文通过Adams 谱序列,发现了球谱S的稳定同伦群中的一族非零元素γth0b21及Toda-Smith谱V(1)的稳定同伦群中的非零元素h0b21.在利用Adams谱序列求解同伦群的过程中,需要计算有关Exts,tA(H*X,H*Y) 的结果.
短句来源
     To determine the stable homotopy groups of spheresπ*S is one of the central problems in homotopy theory. In this paper, it is proved that, for p≥5 to be an arbitrary odd prime number and 1≤s< p, the homotopy elementα1β1βs is nontrivial and of order p in the stable homotopy groups of spheresπ*S.
     决定球面稳定同伦群是同伦论中的核心问题之一,是非常重要的.该文证明:球面稳定同伦元素α1β1βs是一个阶为p的非平凡元素,其中p≥5是任意奇素数,1≤s
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  “同伦群”译为未确定词的双语例句
     Application of Homotopy Theory in Defects of Liquid Crystals
     同伦群理论在液晶缺陷中的应用
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     A New Infinite Family in π_*S~*
     球面稳定同伦群π,S中的一个新非平凡元素族(英文)
短句来源
     This paper proves the existence of a new family of nontrivial homotopy elements in the stable homotopy of spheres which is of degree 2(p-1)(sp 2+(s+1)p+(s-2))-6 and is represented by b 0h 1 s in the E s+3,* 2 -term of the Adams spectral sequence,where p≥7 is an odd prime,3≤s
     证明在Adams谱序列中 ,积b0 h1 γs∈Exts + 3 ,sp2 q + (s+ 1)pq+ (s-2 )q + (s-3 )A (Zp,Zp)收敛到球面稳定同伦群π S中的一个新的非零的稳定元素族 ,其中 3≤s

短句来源
     THE RELATIONS BETWEEN HOMOPTOPY GROUPS AND HOMOLOGY GROUPS,AND SOME OF ITS APPLICATIONS
     同伦群和同调群的关系及其应用
短句来源
     Some New Families in the Stable Homotopy of Spheres Revisited
     球面稳定同伦群的回访新元素族
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  homotopy group
In order for phase transitions to occur, the kinetic part of the action of the system must have conformal invariance, and the vacuum manifold must be degenerate and have a discrete Abelian homotopy group π1.
      
Geometric diffeomorphism finiteness in low dimensions and homotopy group finiteness
      
The first result says that if the Shafarevich Conjecture has an affirmative answer in dimension two then the second homotopy group of a smooth projective surface is a torsion-free abelian group.
      
The structure of the -term indicates that the homotopy group is finite except for i=0,-4 and -5.
      
the first homotopy group of [InlineMediaObject not available: see fulltext.] is trivial.
      
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  homotopy groups
TheE2 term of the spectral sequence of unstable homotopy groups of topological spaces
      
Spectral sequences are constructed and the corresponding homotopy groups are calculated.
      
The corresponding homotopy groups are found for all G.
      
These upper bounds do not depend on X and are given in terms of the exponents of the stable homotopy groups of spheres and, for the last three homomorphisms, in terms of the order of the Postnikov invariants of the spectrum F.
      
Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups.
      
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  group of homotopy
The group of homotopy self-equivalences of some compactCW-complexes
      
Realization problems for the group of homotopy classes of self-equivalences
      
On the group of homotopy equivalences of simply connected five manifolds
      
The group of homotopy equivalences of products of spheres and of Lie groups
      
We establish a braid of interlocking exact sequences containing the group of homotopy self-equivalences of a smooth or topological 4-manifold.
      
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This paper reviewed the progress in the research on the defects of liguid crystals. It discussed the classification of the defects of various kinds of liquid crystals with different dimensions by the homotopy theory. and also discussed the topological property about the strength of the defects.

本文介绍了液晶缺陷研究的进展,并用同伦群理论讨论了各种类型液晶中不同维数的缺陷的分类,还简单讨论了液晶中缺陷强度所遵循的拓扑性质。

A theorem is established that if the topoiogical space V is simply connected, the set of homotopy classes for the S_n→V continuous maps with N(≥1) base points, πn (V; v_1, v_2,…, v_N), can be constructed into group isomorphic to the homotopy group of order n with single base point, π_n(V) (referred to as the homotopy group of order n with N base points). Here, the condition that V is simply connected could not in general be neglected. Some corollaries are given. The application of this theorem and its corollaries...

A theorem is established that if the topoiogical space V is simply connected, the set of homotopy classes for the S_n→V continuous maps with N(≥1) base points, πn (V; v_1, v_2,…, v_N), can be constructed into group isomorphic to the homotopy group of order n with single base point, π_n(V) (referred to as the homotopy group of order n with N base points). Here, the condition that V is simply connected could not in general be neglected. Some corollaries are given. The application of this theorem and its corollaries to the topoiogical classification of magnetization states in ferromagnet is briefly- described with a few examples.

本文建立了一个定理:当拓扑空间V单连通时,N(≥1)基点n阶同伦类集合π_n(V;v_1,v_2,…,v_N)可被构造成同构于单基点n阶同伦群π_n(V)的群,叫做N基点n阶同伦群;并且V的单连通性一般是不可省略的条件。给出了一些推论。简要地触及了这个定理及其推论在铁磁状态拓扑分类中的应用问题。

The parpose of this paper is to introduce an important concepi of fuzzy algebraic topology--the homotopy group of fuzzy topologi-cal space and to show that it is a fuzzy topological invariant.

本文的主要目的是将代数拓扑的n维同伦群推广到F拓扑空间中去且证明是拓扑不变量。

 
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