Abstract and Applied Analysis
Volume 2003 (2003), Issue 2, Pages 121-128
doi:10.1155/S1085337503204024
Connectivity properties for subspaces of function spaces determined by fixed points
Daciberg L. Gonçalves1
and Michael R. Kelly2
1Departamento de Matemática, Instituto de Matemática e Estatistica, Universidade de São Paulo (IME-USP) Caixa Postal 66281, São Paulo, SP, Brazil
2Department of Mathematics and Computer Science, Loyola University, 6363 St. Charles Avenue, New Orleans 70118, LA, USA
Abstract
We study the topology of a subspace of the function space of continuous self-mappings of a given manifold: the subspace determined by maps having the least number of fixed points in its homotopy class. In the case that the manifold is a closed disk of finite dimension, we prove that this subspace is both globally and locally path connected. We also prove this result when the manifold is a sphere of dimension 1, 3, or 7.