Moderately discontinuos algebraic topology for metric subanalytic germs
We have developed both a homology theory and a homotopy theory in the context of metric subanalytic germs (see Definition 2.1). The former is called MD homology and is covered in Chapter 2, which contains a paper that is joined work with my PhD advisors Javier Fernández de Bobadilla and María Pe Per...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | español |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/11043 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/11043 |
| Access Level: | acceso abierto |
| Palabra clave: | 515.14 Algebraic topology homology theory homotopy theory metric subanalytic germs MD homology MD homotopy Topología algebraica teoría de homología teoría de homotopía gérmenes subanalíticos métricos MD homología MD homotopía Álgebra Topología 1201 Álgebra 1210 Topología |
| Sumario: | We have developed both a homology theory and a homotopy theory in the context of metric subanalytic germs (see Definition 2.1). The former is called MD homology and is covered in Chapter 2, which contains a paper that is joined work with my PhD advisors Javier Fernández de Bobadilla and María Pe Pereira and with Edson Sam-paio. The latter is called MD homotopy and is covered in Chapter 3. Both theories are functors from a category of germs of metric subanalytic spaces (resp. germs of metric subanalytic spaces that are punctured in a way that will be defined) to a category of commutative diagrams of groups. For the concrete definition of the domain categories see Definition 2.10 and Definition 3.47 respectively; for the target categories see Definition 2.42 and Definition 3.52 respectively. Similarly to classical homology and homotopy theories, the groups appearing in the target category are abelian in the homology theory for any degree and in the homotopy theory for degree n > 1... |
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