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
Received 31 October 2001

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.