对合的分解  

Decomposition of Involutions

作　　者：干丹岩[1] 

机构地区：[1]浙江大学数学系

出　　处：《Journal of Mathematical Research and Exposition》1991年第1期52-56,共5页数学研究与评论（英文版）

基　　金：国家自然科学基金资助项目

摘　　要：在本文中,我们给出两个n维流形上的对合的双连通和的定义,证明了连通的流形上的对合分解为不可约化的连通的对合的双连通和的存在性和项数的估计.本文主要结果在[2]中宣布过,这里是评细叙述.所论流形均假设为光滑或分片线性流形.因此所涉及的嵌入、同胚及所构作的流形均为光滑的或分片线性的.文中涉及的同调群其系数均取自Z/2Z;当所论流形均为有向时。Using the notion of biconnected sum we define the biconnected sum (T1, M1)§T2,M2) of two involutions (T1M1) and (T2,M2) which is an involution on the biconnected sum M1,§M2. A connected involution is said to be reducible if it can be expressed as a biconnected sum of two connected involutions.Theorem Each connected involution (T, M) can be decomposed into a bi-connected sum of connected irreducible involutionsandwhere the coefficients of Hn_3(M) are in Z/2 Z if M is unoriented, in Z if is oriented .

关 键 词：对合 流形 分解 双连勇和 存在性 

分 类 号：O189.2[理学—数学]