Simplicial homotopy theory
Simplicial homotopy theory
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DOI：
10.1016/0001-8708(71)90015-6
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发表时间：
1968
期刊：
影响因子：
--
通讯作者：
E. Curtis
中科院分区：
文献类型：
--
作者：
E. Curtis
108个CURTIS，满足简单恒等式。S (X)可以用来定义一些常用的不变量（如X的同伦和同调群）和证明一些常用的定理（如Hurewicz定理）。如果X是多面体（有时称为简单复体）的拓扑空间，则存在由X确定的简单集合K，如下所示。对X的顶点排序，对于每一个整数n> 0，令其中vj是一个v < v1<** a< VT的单纯形X的顶点（允许重复），还有面算子和简并算子di: K，-K,-，
108 CURTIS which satisfy the simplicial identities. S (X) can be used to define some of the usual invariants (eg, the homotopy and homology groups of X) and to prove some of the usual theorems (eg, the Hurewicz theorem). If X is the topological space of a polyhedron (sometimes called a simplicial complex), there is a simplicial set K determined by X as follows. Order the vertices of X, and for each integer n> 0, let where the vj are vertices (repetitions allowed) of a simplex of X with v.< v1<** a< VT,. Again there are face and degeneracy operators di: K,-K,-,,