论文标题
立方组的同型组
Homotopy groups of cubical sets
论文作者
论文摘要
我们定义和研究立方组的同喻组。为此，我们给出了立方体集合的同副群组的四个定义，证明它们是等效的，进一步通过几何实现函数同意了拓扑类似物的一致。我们还提供了几种经典定理的纯粹组合证明，包括：产品保存，较高同型基团的通勤性，纤维化的长序列和Whitehead定理。这是我们“离散同义理论的立方环境”的同伴论文，其中我们将这些结果应用于研究简单图的同喻理论。
We define and study homotopy groups of cubical sets. To this end, we give four definitions of homotopy groups of a cubical set, prove that they are equivalent, and further that they agree with their topological analogues via the geometric realization functor. We also provide purely combinatorial proofs of several classical theorems, including: product preservation, commutativity of higher homotopy groups, the long exact sequence of a fibration, and Whitehead's theorem. This is a companion paper to our "Cubical setting for discrete homotopy theory, revisited" in which we apply these results to study the homotopy theory of simple graphs.
