Connectivity properties for subspaces of function spacesdetermined by fixed points

[摘要] We study the topology of a subspace of the function space ofcontinuous self-mappings of a given manifold: the subspacedetermined by maps having the least number of fixed points in itshomotopy class. In the case that the manifold is a closed disk offinite dimension, we prove that this subspace is both globallyand locally path connected. We also prove this result when themanifold is a sphere of dimension 1, 3, or 7.

[学科分类] 数学（综合）