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Bott\'s periodicity theorem from the algebraic topology viewpoint

Bonatto, Luciana Basualdo

Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Matemática e Estatística 2017-08-23

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Título:
Bott\'s periodicity theorem from the algebraic topology viewpoint
Autor: Bonatto, Luciana Basualdo
Orientador: Struchiner, Ivan
Assuntos: Teoria De Morse-Bott; Cohomologia Generalizada; Teoria De Morse; Espaços De Eilenberg-Maclane; Teoria De Homotopia; Teorema Da Periodicidade De Bott; K-Teoria; Sequências Espectrais; Spectral Sequences; Morse-Bott Theory; Morse Theory; K-Theory; Homotopy Theory; Generalised Cohomology; Eilenberg-Maclane Spaces; Botts Periodicity Theorem
Descrição: In 1970, Raoul Bott published The Periodicity Theorem for the Classical Groups and Some of Its Applications, in which he uses this famous result as a guideline to present some important areas and tools of Algebraic Topology. This dissertation aims to use the path Bott presented in his article as a guideline to address certain topics on Algebraic Topology. We start this incursion developing important tools used in Homotopy Theory such as spectral sequences and Eilenberg-MacLane spaces, exploring how they can be combined to aid in computation of homotopy groups. We then study important results of Morse Theory, a tool which was in the centre of Botts proof of the Periodicity Theorem. We also develop two extensions: Morse-Bott Theory, and the applications of such results to the loopspace of a manifold. We end by giving an introduction to generalised cohomology theories and K-Theory.
DOI: 10.11606/D.45.2017.tde-17112017-130250
Editor: Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Matemática e Estatística
Data de criação/publicação: 2017-08-23
Formato: Adobe PDF
Idioma: Inglês

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Bott\'s periodicity theorem from the algebraic topology viewpoint

Bonatto, Luciana Basualdo

Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Matemática e Estatística 2017-08-23

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