The fixed point property in every weak homotopy type

We prove that for any connected compact CW-complex K there exists aspace X weak homotopy equivalent to K which has the fixed point property, that is,every continuous map X -> X has a fixed point. The result is known to be false if werequire X to be a polyhedron. The space X we construct is a non-...

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Detalhes bibliográficos
Autor: Barmak, Jonathan Ariel
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/18909
Acesso em linha:http://hdl.handle.net/11336/18909
Access Level:acceso abierto
Palavra-chave:FIXED POINT PROPERTY
SIMPLICIAL COMPLEXES
WEAK HOMOTOPY TYPES
FINITE TOPOLOGICAL SPACES
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descrição
Resumo:We prove that for any connected compact CW-complex K there exists aspace X weak homotopy equivalent to K which has the fixed point property, that is,every continuous map X -> X has a fixed point. The result is known to be false if werequire X to be a polyhedron. The space X we construct is a non-Hausdorff space withfinitely many points.