Singularidades de aplicações de reflexão

• Ano de defesa: 2025
• Autor(a) principal: Gama, Milena Barbosa
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Geometria; Topologia; Matriz de apresentação; Aplicação de reflexão; Grupo de reflexão; Reflection map; Reflection group; Presentation matrix; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/123456789/37205

In this work, we consider some problems related to germs of reflected graph maps f, from (Cn, 0) to (Cn+1 , 0). A reflected graph map is a particular case of a reflection map, defined as the composition of the map induced by the action of a reflection group G on Cn+1 with an embedding of Cn into Cn+1 . In this work, we present a description of the presentation matrix of f⋆On as an On+1-module via f, in terms of the action of the associated reflection group G. As a consequence, we also provide a defining equation for the image of f, again in terms of the action of G. Moreover, we present upper and lower bounds for the multiplicity of the image of f, along with some applications. Finally, we introduce a new class of map germs, called “2m-dihedral map germs” and we apply the results obtained to study this class of maps.