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Integración con respecto a la característica de Euler-Poincaré
- Autor/a
- Mosquera Lois, David
The aim of this dissertation is to develop an integration theory against the Euler-Poincaré characteristic. Several families of topological spaces and definitions of the Euler characteristic for them are introduced, mainly a combinatorial and a (co)homological definition. Integration against Euler-Poincaré characteristic is defined and several properties are discussed. Finally, applications of the theory previously exposed are studied, both in the context of target enumeration in sensor networks and in Geometry and Topology. Particularly, alternative proofs of the Riemann-Hurwitz formula and of the characteristic of a fiber bundle are presented. Furthermore, it is introduced a generalization of the class of spaces for which the integration against the Euler characteristic is defined.
Data sheet
- Edition
- 1
- Publication place
- Santiago de Compostela
- Publication Year
- 07/03/2018
- Serie
- 133a Publicaciones del Departamento de Geometría y Topología
- ISBN
- 9788489390508
- Availability
- Si
The aim of this dissertation is to develop an integration theory against the Euler-Poincaré characteristic. Several families of topological spaces and definitions of the Euler characteristic for them are introduced, mainly a combinatorial and a (co)homological definition. Integration against Euler-Poincaré characteristic is defined and several properties are discussed. Finally, applications of the theory previously exposed are studied, both in the context of target enumeration in sensor networks and in Geometry and Topology. Particularly, alternative proofs of the Riemann-Hurwitz formula and of the characteristic of a fiber bundle are presented. Furthermore, it is introduced a generalization of the class of&n