On the Pontryagin product in spaces of paths
On the Pontryagin product in spaces of paths
复制标题
路径空间中的庞特里亚金积
DOI：
10.1007/bf02564566
复制
发表时间：
1953
影响因子：
0.9
通讯作者：
H. Samelson
中科院分区：
文献类型：
--
作者：
R. Bott;H. Samelson
对于拓扑（弧连通）空间X，设E是由X中从某一点x开始的路径组成的函数空间，设~ 9是E的由闭路径或环组成的子空间; M.莫尔斯[7]和J. - P. Serre [10]; E是X上的纤维空间。现在~ 9允许自然相乘：连续两个循环构成一个新循环（实际上E和~ 9之间存在更通用的运算）。这一增长带来了多重--
For a topological (arcwise connected) space X, let E be the function space consisting of the paths in X which start at a certain point x, and let~ 9 be the subspace of E consisting of the closed paths or loops; these spaces have been studied in particular by M. Morse [7] and J.-P. Serre [10]; E is a fiber space over X. Now~ 9 admits a natural multiplication: two loops in succession make a new loop (actually there is a more general operation between E and~ 9). This multiplication gives rise to a multi-