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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2020.tde-19052020-183114
Document
Author
Full name
Bartira Maués
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2020
Supervisor
Committee
Goncalves, Daciberg Lima (President)
Borsari, Lucilia Daruiz
Manzoli Neto, Oziride
Pereiro, Carolina de Miranda e
Vendruscolo, Daniel
Title in English
Nielsen theory of 2-valued maps on the Klein bottle
Keywords in English
Braidgroups
Equations in free groups
Klein-bottle
Multivalued maps
Nielsen number
Wecken property
Abstract in English
In this work we study 2-valued maps on the Klein-bottle using braid theory. We provide a classification of based homotopy classes of split (2-valued) maps with Nielsen number zero in terms of the pure braid group with two strings on the Klein-bottle. We give necessary conditions, in terms of the total braid group, for maps that are non-split and compute their Nielsen number. For compact manifolds X and Y we establish a connection between 2-valued non-split maps from X to Y, and classes of maps from X' to Y that have not the Borsuk-Ulam property in respect to the deck-transformation given by a certain covering space q:X'->X.
Title in Portuguese
Teoria de Nielsen de funções à dois valores na garrafa de Klein
Keywords in Portuguese
Equações em grupos livres
Funções multivaluadas
Garrafa de Klein
Grupo de tranças
Número de Nielsen
Propriedade de Wecken
Abstract in Portuguese
Nesse trabalho estudamos funções (contínuas) à dois valores na garrafa de Klein usando teoria de tranças. Classificamos homotopicamente as funções (à dois valores) com número de Nielsen zero em termos do grupo das tranças puras de duas cordas da garrafa de Klein. Damos condições necessárias para funções que não são split em termos do grupo total de tranças e calculamos o número de Nielsen das funçoes que não são split. Para variedades compactas X e Y estabelecemos uma conexão entre uma função à dois valores de X em Y e classes de funções de X' em Y que não tem a propriedade Borsuk-Ulam com respeito à transformação de recobrimento dada por um recobrimento específico q:X'->X.
 
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Tese_BartiraMaues.pdf (793.62 Kbytes)
Publishing Date
2021-01-20
 
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