论文标题
纠正交织和持续的白头定理
Rectification of interleavings and a persistent Whitehead theorem
论文作者
论文摘要
同型交织距离是布伦伯格和莱斯尼克引入持续空间之间的距离，并被证明是通用的，从某种意义上说，它是最大的同型不变性距离，其近距离实现功能的超级速度过滤是接近的。还有其他方法可以构建同二次不变的距离，但是对于这些选择之间的关系并不了解。我们表明，其他自然距离与最多乘法常数的同质性交织距离有所不同，并证明了持续的白头定理的版本，blumberg and Lesnick的猜想与形态学相关，这些形态与持久的同质群体中的同质概念相互互动的概念引起了持久的同质群。
The homotopy interleaving distance, a distance between persistent spaces, was introduced by Blumberg and Lesnick and shown to be universal, in the sense that it is the largest homotopy-invariant distance for which sublevel-set filtrations of close-by real-valued functions are close-by. There are other ways of constructing homotopy-invariant distances, but not much is known about the relationships between these choices. We show that other natural distances differ from the homotopy interleaving distance in at most a multiplicative constant, and prove versions of the persistent Whitehead theorem, a conjecture of Blumberg and Lesnick that relates morphisms that induce interleavings in persistent homotopy groups to stronger homotopy-invariant notions of interleaving.
