Mathematical Sciences: Cohomological Dimension

数学科学：上同调维数

• 批准号: 9101283
• 负责人: Jerzy Dydak
• 金额: $ 5.19万
• 依托单位: University of Tennessee Knoxville
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101283&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Cohomological; Dimension

This research concentrates on algebraic aspects of dimension theory. The crucial part of the project is to decide whether cell- like images of euclidean 4-space are finite-dimensional. Proving (or disproving) results in cohomological dimension theory which are analogous to results in covering dimension theory is another goal of the project. The answers are known to the analogues of the key question for Euclidean spaces of dimensions other than 4. This is another case where the difficulty of a topological question does not increase with dimension. It is distressing to find that the greatest mysteries concern the space of three dimensions in which we live or the space of four dimensions, which may be viewed as space-time.

本研究集中在维数的代数方面 理论 该项目的关键部分是决定细胞- 欧氏四维空间的相似图像是有限维的。 证明 (or反证）的结果在上同调维数理论， 与覆盖维数理论的结果类似， 本项目 答案是已知的类似的关键问题， 4维以外的欧几里得空间。 这是另一个案子 拓扑问题的难度不会增加 的尺寸。 令人痛心的是， 我们生活的三维空间的奥秘， 四维空间，可以被看作是时空。