Harmonic morphisms with one-dimensional fibres on Einstein manifolds

We prove that, from an Einstein manifold of dimension greater than or equal to five, there are just two types of harmonic morphism with one-dimensional fibres. This generalizes a result of R.L. Bryant who obtained the same conclusion under the assumption that the domain has constant curvature.

     

预加法范畴中态射的(1,2)-逆与βα(1,2)γ的不变性

研究了预加法范畴中态射的(1,…,i)-逆,给出了态射三乘积βα′γ的不变性的充要条件,其中α′是态射α的(1)-逆或者(1,2)-逆。     

同伦正则态射的若干性质

首先证明了点标拓扑空间的笛卡尔积保持同伦正则性,继而证明了Sm ash积也保持同伦正则,最后就函数空间讨论了同伦正则性.由此,得到了比现有文献中闭路函子和同纬函子保持同伦正则性更为一般的结果.     

倾斜代数和预投射分支中模的一些性质

证明了倾斜代数含有一个连接分支Г,并且在这一分支中,从内射模到投射模的路(若有)都是截口路.还证明了预投射分支中模的既约前趋的个数是有限的,且有rad∞(@,X)=0,其中X为此分支中的模.     

关于调和射的一个整体构造

利用了经典Ｈｏｐｆ纤维化π：Ｓ＾７→Ｓ＾４，构造了Ｓ＾８→－Ｓ＾５的整体调和射。     

A morphism of intersection homology induced by an algebraic map

Let be a map of algebraic varieties. Barthel, Brasselet, Fieseler, Gabber and Kaup have shown that there exists a homomorphism of intersection homology groups compatible with the induced homomorphism on cohomology. The crucial point in the argument is reduction to the finite characteristic. We give an alternative and short proof of the existence of a homomorphism . Our construction is an easy application of the Decomposition Theorem.

     

一种特殊Reinhardt域的解析自同构最大群

本文给出了域Ｄ＝｛ｚ＝（ｚ１，ｚ２，ｚ３）∈Ｃ３：｜ｚ１｜＋｜ｚ２｜＋｜ｚ３｜２＜１｝上的Ｂｅｒｇｍａｎ核函数和解析自同构最大群．     

-coarse geometry of complements of Z-sets in the Hilbert cube

Motivated by the Chapman Complement Theorem, we construct an isomorphism between the topological category of compact Z-sets in the Hilbert cube and the -coarse category of their complements. The -coarse morphisms are, in this particular case, intrinsically related to uniformly continuous proper maps. Using that fact we are able to relate in a natural way some of the topological invariants of Z-sets to the geometry of their complements.

     

具有泛分解态射的加权Moore-Penrose逆

讨论了预加法范畴C中具有泛分解态射的加权Moore-Penrose逆,并给出了具有泛分解态射的加权Moore-Penrose逆存在的几个充要条件,以及具有泛分解态射的加权Moore-Penrose逆的表达式,推广了关于具有泛分解态射的广义Moore-Penrose逆的相应结果.     

同纬映象函子与同伦正则态射

利用同纬映象函子定义稳定同伦正则态射, 并研究了稳定同伦正则态射存在的条件及性质, 得到如下结果： 若态射f: X→Y有稳定同伦标准分解 (g,Z,h), 设有A,B及相应的态射i: A→X与p: Y→B, 使得gi和ph是稳定同伦等价的, 则f: X→Y必为稳定同伦正则态射, 且在k稳定同伦意义下惟一.