论文标题
缩水根本没有做很多事情
Shrinking Without Doing Much At All
论文作者
论文摘要
1952年，宾（Bing）以$ s^3 $的疯狂涉嫌使数学世界感到惊讶。它一直是拓扑结构中最开创性的例子之一。该示例取决于发现Bing分解$ s^3 $的同态形态的缩小。如果Bing的原始同态形态变化，Bing的原始野生涉及通过共轭发生了变化，从而保留了某些分析属性\ cite {fs22}，同时更改了其他分析。 1988年，Bing发表了第二篇论文“缩小而没有延长”，回答了一个问题，其中一位作者向他提出了一个努力，以了解整个共轭班的几何形状。在本文中，我们产生了一种违反直觉的结构，即一种缩小bing分解几乎没有做任何事情的方法 - 不会延长太多，也不会旋转太多。
In 1952 Bing astonished the mathematical world with his wild involution on $S^3$. It has been among the most seminal examples in topology. The example depends on finding shrinking homeomorphisms of Bing's decomposition of $S^3$ into points and arcs. If Bing's original homeomorphisms are varied, Bing's original wild involution changes by conjugation, which preserves some analytic properties \cite{fs22} while altering others. In 1988, Bing published a second paper "Shrinking Without Lengthening," answering a question that one of the present authors posed to him in an effort to understand the geometry of the entire conjugacy class. In this paper we produce a counterintuitive construction, namely, a method to shrink the Bing decomposition doing almost nothing at all--neither lengthening much nor rotating much.
