Topics in Topological Fixed Point Theory

拓扑不动点理论专题

• 批准号: 0805968
• 负责人: Peter Wong
• 金额: $ 10.72万
• 依托单位: Bates College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0805968&HistoricalAwards=false
• 关键词: Topics; Topological; Fixed; Point; Theory

One of the central issues in fixed point theory is to compute the Nielsen number of a self map of a compact manifold X. This problem is closely related to understanding induced twisted conjugacy classes in the fundamental group of X. A related question is the coincidence problem of two maps from X to Y. A special case is a Borsuk-Ulam type problem. Wong proposes three sets of problems on (i) the study of the Reidemeister number; (ii) the study of the positive codimensional coincidence problem when the dimension of X is greater than that of Y ; and (iii) combinatorial approaches to Borsuk-Ulam type problems.Topological fixed point theory is a classical topic which generated much research in algebraic topology during the first half of the twentieth century. This proposal concerns the calculation of Nielsen numbers, an invariant in fixed point theory. Nielsen numbers have been shown to have applications in dynamical sysytems and nonlinear analysis. Wong proposes to study Nielsen numbers in some especially difficult situations where another more easily computed invariant, the Reidemister number, may differ from the Nielsen number. Combinatorial approaches to these calculations are also envisioned.

固定点理论中的一个中心问题是计算紧凑型歧管X的自我图的尼尔森数量。该问题与理解X基本组的诱导的扭曲的共轭类密切相关。一个相关的问题是两个地图的巧合问题。从x到y的两个地图的巧合问题。一个特殊情况是Borsuk-Ulam类型问题。 Wong提出了（i）研究中的三组问题； （ii）当x的尺寸大于y的尺寸时，对正编成巧合问题的研究； （iii）Borsuk-Ulam类型问题的组合方法。togologicy固定点理论是一个经典的主题，在20世纪上半叶，在代数拓扑中产生了许多研究。该提案涉及尼尔森数字的计算，尼尔森数字是固定点理论中不变的。尼尔森的数量已显示在动态系统和非线性分析中具有应用。 Wong建议在某些特别困难的情况下研究Nielsen的数字，在某种情况下，另一个更容易计算出的不变式的重新住房数字可能与Nielsen数字有所不同。还设想了这些计算的组合方法。