同伦群

多基点同伦群理论

The theory of homotopy group with multiple base points

同伦论的重要内容就是计算空间的同伦群，目前计算同伦群的最重要方法是谱序列。

The most important content in Homotopy theory is to calculate the homotopy group of a topological space . Now the most useful method to calculate homotopy group is spectral sequence .

球面稳定同伦群中的一个新元素族b1g0（γ~）s

A new family represented by b_1g_0 (γ | - ) _s in the Stable Homotopy Groups of spheres

并进一步证明了在复平面C上，任意区域的拓扑边界上的连续函数代数的K1群与它边界上的同伦群同构。

And prove that the cohomotopy groups is isomorphic to K_1-group of the continuous algebra on topological boundary of domains in C.

本文证明：当p≥7任意奇素数，3≤s球面稳定同伦群πS中的一个阶为p的非平凡元素。

In this paper , it is proved that for p ≥ 7 an arbitrary odd prime number and 3 ≤ s < p , the homotopy element α 1 β 1 γ s is nontrivial and of order p in the stable homotopy groups of spheres π S.

运用Yoneda乘积，得到了球面稳定同伦群中的一个非零元素g0（b1）4γs~。

With the help of ( Yoneda ) - products , a nonzero element g_0 ( b_1 ) ~ 4_s of stable homotopy groups of sphere is obtained .

上同调算子也是同伦论的一部分重要内容，可以用来计算空间的同伦群，并且与相应的Eilenberg-MacLane空间的上同调群存在双射。

Cohomology operation belongs to Homotopy theory and can be used to calculate the homotopy group of topological space . Further more it has a bijection relationship with the cohomology group of the corresponding Eilenberg-MacLane space .

球面稳定同伦群的回访新元素族

Some New Families in the Stable Homotopy of Spheres Revisited

同伦群理论在液晶缺陷中的应用

Application of Homotopy Theory in Defects of Liquid Crystals

关于球面非零同伦群的若干结果

Some results of non-zero Homotopy Groups of spheres

球面稳定同伦群π，S中的一个新非平凡元素族（英文）

A New Infinite Family in π _S ~

同伦群和上同调群的上乘积

Homotopy Groups and cup product of cohomology groups

球上同伦群的不变量玻璃钢球罐设计

Design of GRP Globe Tank