论文标题
持续同义理论
Persistent homotopy theory
论文作者
论文摘要
越野裂和程度撕裂复合物通过其基本的简单效果表示为同型类型，并且在这些术语中，基本同质稳定性定理是重新铸造的。这些同质类型被视为在参数空间上定义的系统（或函子）。空间系统的类别承认了一种基于受控等价（适当定义）的部分同位拷贝理论，该理论是同质稳定性结果的输出。
Vietoris-Rips and degree Rips complexes are represented as homotopy types by their underlying posets of simplices, and basic homotopy stability theorems are recast in these terms. These homotopy types are viewed as systems (or functors), which are defined on a parameter space. The category of systems of spaces admits a partial homotopy theory that is based on controlled equivalences, suitably defined, that are the output of homotopy stability results.
