Connectivity properties for subspaces of function spacesdetermined by fixed points

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...

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Bibliographic Details
Published in:Abstract and applied analysis 2003-01, Vol.2003 (2), p.121-128
Main Authors: Gonçalves, Daciberg L., Kelly, Michael R.
Format: Article
Language:English
Online Access:Get full text
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/S1085337503204024