廖山涛教授的代数拓扑研究工作

The Research Works of Professor S.D. Liao in Algebraic Topology

§1 局部乘积与Poincar6-A1exande-Lefschetz型对偶定理 设x为紧致Hausdotff空间,X_0,E为X的闭子集.证E_0=X_0∩E_0.(X_0,E_0)在(X,E)中以G为系数群的局部上、下同调群H^i(X_0|x,E;G)、Hi(X_0|X,E_0|E;G)已有定义.一空间在一子集处的局部同调群的运用早已隐含在Lefschetz①和Wilder②的书中,设G_1,G_2,G_0为系数群,且有配对G_1·G2→G_0,廖山涛在局部同调群中进一步引入局部上积与卡积如下:

In this paper, the research works of professor S.D.Liao are introduced, including the following fields. (1) on local products and duality of Poincare-Alexan-der-Lefschetz type; (2) periodic transformations and fixed point theorems; (3) the cyclic products of spheres and the theory of obstruction of sphere bundles.