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.
