Topics in Topological Fixed Point Theory

不动点理论的核心问题之一是计算紧流形X的自映射的Nielsen数，这一问题与理解X的基本群中的诱导扭曲共轭类密切相关。一个相关的问题是X到y的两个映射的重合问题，一个特殊的例子是Borsuk-Ulam型问题。Wong提出了三组问题：(i)对Reidemeister数的研究；（ii）当X的维数大于Y的维数时的正协维重合问题的研究；（iii） Borsuk-Ulam型问题的组合方法。拓扑不动点理论是20世纪上半叶代数拓扑学研究的一个经典课题。本文讨论了不动点理论中不变量尼尔森数的计算。尼尔森数已被证明在动力系统和非线性分析中有应用。Wong建议在一些特别困难的情况下研究尼尔森数，在这些情况下，另一个更容易计算的不变量Reidemister数可能与尼尔森数不同。还设想了这些计算的组合方法。

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.