Homologia métrica
In this paper we develop and apply the theory of homology metric, created by Jean Paul Brasselet and Lev Birbrair. Each set semialgébrico X associate a collection of real vector spaces (or abelian groups) ^ {MH_k ν (X)} _ {k} є Z so that it is given another semialgébrico X 'semialgebricamente w...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | Brasil |
| Institución: | Universidade Federal do Ceará (UFC) |
| Repositorio: | Repositório Institucional da Universidade Federal do Ceará (UFC) |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufc.br:riufc/964 |
| Acceso en línea: | http://www.repositorio.ufc.br/handle/riufc/964 |
| Access Level: | acceso abierto |
| Palabra clave: | Singularidades Espaços vetoriais Grupos abelianos Topologia algébrica |
| Sumario: | In this paper we develop and apply the theory of homology metric, created by Jean Paul Brasselet and Lev Birbrair. Each set semialgébrico X associate a collection of real vector spaces (or abelian groups) ^ {MH_k ν (X)} _ {k} є Z so that it is given another semialgébrico X 'semialgebricamente which is bi-Lipschitz equivalent to X, then ν MH_k ^ (X) is isomorphic to MH_k ν ^ (X ') for all k. Thus, the collection {^ MH_k ν (X)} carries some information metric semialgébrico X. In particular, we have necessary conditions for an isolated singularity x_0 belonging to X is conical. More precisely, given a submanifold compact L of a sphere S_ {x_0, r}, we compute the groups MH_k ^ ν (x_0 * L) in terms of singular homology of L, where x_0 * L denotes the cone {tx_0 + (1-t ) x, x belonging to L, t belonging to [0,1]}. Allied to the metric we have the homology cycles Chegger, geometric objects that obstruct the nature of a conical singularity. As an application of the theory, we present a class of complex surfaces whose singularities (isolated) are non-tapered. |
|---|