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Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.2020.tde-18022020-103740
Document
Author
Full name
Carlos Biasi
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1981
Supervisor
Committee
Loibel, Gilberto Francisco (President)
Conde, Antonio
Daccach, Janey Antonio
Favaro, Luiz Antonio
Saab, Mario Rameh
Title in Portuguese
L - EQUIVALÊNCIA E BORDISMO AMBIENTAL DE SUBVARIEDADES
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Não disponível
Title in English
Not available
Keywords in English
Not available
Abstract in English
The concepts of L-equivalence of submanifolds (due to R. Thom) and ambiental bordism of submanifolds will be the main objects of this thesis. Let Nn be an oriented manifoid, Lk(N) the set of L-equivalence classes of compact oriented submanifolds Kk ⊂ N and Ωk (N) the Kth oriented bordism group of N. There is a natural map Φ : Lk (N) → Ωk (N). One of the main results is the following theorem: "If n ≥ 2k, there is a geometric group structure on Lk(N) such that Φ is an isomorphism. In particular, if N = S2k there is an isomorphism π2K(MS0(k)) ≈ Ωk". The main result about ambiental bordism is the following: Let n = 2k+1, Nn a compact oriented manifold and Kk a compact oriented submanifold of N. Then K bounds in N if and only if Φ([K]) = O, where [K] is the L-equivalence class of K".
 
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CarlosBiasi_DO.pdf (2.49 Mbytes)
Publishing Date
2020-02-18
 
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