Análise em variedades topológicas
This dissertation consists of a detailed study on a series of results published in the last ten years on maps between topological manifolds, with focus in the so called homological version of the famous inverse and implicit mapping theorem. With an approach which in- volves differential and homologi...
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| Tipo de documento: | dissertação |
| Estado: | Versão publicada |
| Data de publicação: | 2018 |
| País: | Brasil |
| Recursos: | Universidade Federal de Uberlândia (UFU) |
| Repositório: | Repositório Institucional da UFU |
| Idioma: | português |
| OAI Identifier: | oai:repositorio.ufu.br:123456789/22028 |
| Acesso em linha: | https://repositorio.ufu.br/handle/123456789/22028 http://dx.doi.org/10.14393/ufu.di.2018.1162 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Orientação de variedades topológicas Orientation of topological manifolds Grau de uma aplicação Degree of maps Teorema da aplicação implı́cita Implicit mapping theorem Teorema da aplicação inversa Inverse mapping theorem Formas locais das imersões e submersões Local imersions and submersions forms CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA::TOPOLOGIA ALGEBRICA |
| Resumo: | This dissertation consists of a detailed study on a series of results published in the last ten years on maps between topological manifolds, with focus in the so called homological version of the famous inverse and implicit mapping theorem. With an approach which in- volves differential and homological techniques, we present a version of the inverse mapping theorem for differential maps which are not necessarily continuously differentiable. As a consequence, we improve the known differential version of the implicit mapping theorem and we present an existence and uniqueness theorem for certain differential equations. |
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