Obstruction theory for coincidences of multiple maps

Let f1,…,fk:X→N be maps from a complex X to a compact manifold N, k≥2. In previous works [1,12], a Lefschetz type theorem was established so that the non-vanishing of a Lefschetz type coincidence class L(f1,…,fk) implies the existence of a coincidence x∈X such that f1(x)=…=fk(x). In this paper, we i...

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Detalles Bibliográficos
Autores: Monis, Thaís F.M. [UNESP], Wong, Peter
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/169999
Acceso en línea:http://dx.doi.org/10.1016/j.topol.2017.07.017
http://hdl.handle.net/11449/169999
Access Level:acceso abierto
Palabra clave:Lefschetz coincidence theory
Local coefficients
Obstruction theory
Descripción
Sumario:Let f1,…,fk:X→N be maps from a complex X to a compact manifold N, k≥2. In previous works [1,12], a Lefschetz type theorem was established so that the non-vanishing of a Lefschetz type coincidence class L(f1,…,fk) implies the existence of a coincidence x∈X such that f1(x)=…=fk(x). In this paper, we investigate the converse of the Lefschetz coincidence theorem for multiple maps. In particular, we study the obstruction to deforming the maps f1,…,fk to be coincidence free. We construct an example of two maps f1,f2:M→T from a sympletic 4-manifold M to the 2-torus T such that f1 and f2 cannot be homotopic to coincidence free maps but for any f:M→T, the maps f1,f2,f are deformable to be coincidence free.