Torsion invariant on cellular complexes

• Ano de defesa: 2024
• Autor(a) principal: Santos, Gustavo de Oliveira Cardoso dos
• Orientador(a): Hartmann Junior, Luiz Roberto
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de São Carlos; Câmpus São Carlos
• Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática - PPGM
• Palavras-chave em Português: CW-complexos; Dualidade de Poincaré; Grupos de Whitehead; Pseudovariedades; Torção de Reidemeister; Torção de Reidemeister de interseção; Torção de Whitehead
• Palavras-chave em Inglês: CW-complexes; Poincaré duality; Whitehead groups; Pseudomanifolds; Reidemeister torsion; Intersection Reidemeister torsion; Whitehead torsion
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA; CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA::TOPOLOGIA ALGEBRICA
• Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/20770

Classifying spaces up to homeomorphism, homotopy equivalence, or combinatorial equivalence is one of the main problems in Topology. To achieve this, we have several invariants in Algebraic Topology, such as Euler characteristic, homotopy groups, homology groups and cohomology groups. In 1935, K. Reidemeister published a work on the classification of a certain class of 3-manifolds that have isomorphic homology groups and homotopy groups but are not homeomorphic. Some of them do not even have the same type of homotopy. For this classification, Reidemeister used a combinato- rial/topological invariant called torsion invariant. Based in [20], [18], [19] and [13], we will discuss here some versions of this invariant for CW-complexes, namely Whitehead torsion, Reidemeister torsion, and Reidemeister intersection torsion for pseudomanifolds with isolated singularities.