G-actions on disks and permutation representations
G-actions on disks and permutation representations
复制标题
磁盘上的 G 动作和排列表示
DOI：
10.1016/0021-8693(78)90173-4
复制
发表时间：
1978
影响因子：
0.9
通讯作者：
R. Oliver
中科院分区：
文献类型：
--
作者：
R. Oliver
有限群G的Burnside环Q (G)是原始的！-定义为C；所有有限g集（具有g作用的有限集）上的rothendieck群，由不相交并和b！(“自廉的产品。torn Dicck 121最近给出了这个环的拓扑定义：取所有紧致光滑g流形的catqjl -\， an<。1 idcntif ?es t \ \ om;mifolcis-If,, ind. li，如果欧拉特征x （; ll, ' '）和x(。11, ")对所有/I (;（additicjl；和乘法定义为-c）都相等。“l 'hc corrcspondcncc bctn ecn: n(1定义是pivcn我,\ -rcgardinq有限C-sct5作为zero-dilncnsional manif[,摩门教。
‘I’hc Burnside ring Q (G) of a finite group G was originall!-defined as the C; rothendieck group on all finite G-sets (finite sets with G-action), with addition induced by disjoint union and multiplication b!.(‘artesian product. torn Dicck 121 has recently given a topological definition for this ring: one takes the catcqJl-\of all compact smooth G-manifolds, an<. 1 idcntif? es t\\om; mifolcis-If,, ind. li, if the Euler characteristics x (; ll,“) and x (. 11,“) are equal for all/I (;(additicjl; and multiplication are defined as betin-c).‘l’hc corrcspondcncc bctn ecn: n (1 definitions is pivcn I,\-rcgardinq finite C-sct5 as zero-dilncnsional manif [, lds.