可缩空间与结合同伦
Contractible spaces and coalescent homotopies
摘要：
本文讨论了可缩空间的合并压缩的存在性和不存在性。这些收缩使得当任何两点的轨迹在时间t0相遇时，它们此后保持在一起。如果一个有限单纯复形K是可塌缩的，那么K的任何塌缩都编码了K的合并收缩。不存在结合收缩的可缩空间的例子是傻瓜帽和宾的房子。我们建立了一个可收缩的有限单纯复形的标准，确保没有合并收缩：星盘属性。关键词：可缩空间，结合同伦，傻瓜帽，宾的房子。
英文摘要：
This paper deals with the existence, or absence, of coalescent contractions of contractible spaces. These are the contractions such that when the tracks of any two points meet, at time t0, they remain together thereafter. If a finite simplicial complex K is collapsible, then any collapse of K encodes coalescent contractions of K. Examples of contractible spaces where no coalescent contractions exist are the Dunce Hat and Bing's house. We establish a criteria for contractible finite simplicial complexes that ensures there are no coalescent contractions: the star-disc property. Keywords: contractible spaces, coalescent homotopies, dunce hat, Bing's house.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
