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Doctoral Thesis
DOI
10.11606/T.45.2017.tde-08122017-142905
Document
Author
Full name
Gustavo de Lima Prado
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2015
Supervisor
Committee
Goncalves, Daciberg Lima (President)
Borsari, Lucilia Daruiz
Libardi, Alice Kimie Miwa
Manzoli Neto, Oziride
Pergher, Pedro Luiz Queiroz
Title in Portuguese
Coincidências em codimensão um e bordismo
Keywords in Portuguese
bordismo normal
cobordismo normal.
codimensão um
coincidência
fibração
propriedade de Wecken
raiz
Abstract in Portuguese
Neste trabalho, estudamos coincidências entre duas aplicações contínuas f e g, de X em Y, onde X e Y são variedades diferenciáveis, conexas, sendo X fechada (n+1)-dimensional e Y sem bordo n-dimensional. Quando o domínio é a esfera e g é constante, consideramos homomorfismos w' e w'' que juntos determinam o invariante de bordismo normal do par (f,g). Calculamos w'' para vários espaços e, em particular, para fibrados esféricos sobre esferas, obtemos que w'' é identicamente nulo se, e somente se, Y é trivial ou Y não é um S²-fibrado sobre S⁴. Finalmente, obtemos resultados tipo Wecken quando X é a esfera, e quando X é o espaço projetivo real de dimensão 3 e Y é a esfera de dimensão 2.
Title in English
Coincidences in codimension one and bordism
Keywords in English
codimension one
coincidence
fibration
normal bordism
normal cobordism.
root
Wecken property
Abstract in English
In this work, we study coincidences between two maps f and g, from X to Y, where X and Y are smooth manifolds, connected, being X closed (n+1)-dimensional and Y without boundary n-dimensional. When the domain is the sphere and g is constant, we consider homomorphisms w' and w'' which together determine the normal bordism invariant of the pair (f,g). We calculate w'' for several spaces and, in particular, for sphere bundles over spheres, we obtain that w'' is identically null if and only if Y is trivial or Y is not an S²-bundle over S⁴. Finally, we obtain Wecken type results when X is the sphere, and when X is the 3-dimensional real projective space and Y is the 2-dimensional sphere.
 
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Publishing Date
2017-12-13
 
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