Amb motiu del tancament d'estiu, la validació de documents es reprendrà a partir del 28 d'agost de 2026. Disculpeu les molèsties.
Con motivo del cierre de verano, la validación de documentos se reanudará a partir del 28 de agosto de 2026. Disculpad las molestias
Due to the summer closure, document validation will resume starting August 28, 2026. We apologize for any inconvenience.

Document type

Bachelor thesis

Publication date

Publication license

cc-by-nc-nd (c) Onofre Bisbal Castañer, 2023
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/198338

La successió espectral de Serre i algunes aplicacions

Journal Title

Journal ISSN

Volume Title

Related resource

Abstract

[en] The aim of this work is to introduce Serre’s spectral sequence. Spectral sequences are a very powerful tool that allows us to relate the homology (or cohomology) groups of various topological spaces when we cannot do so using other simpler methods such as exact couples. The basic idea is to calculate successive approximations of the invariant we want to find, so that each term increases the level of precision, until we obtain it in the most favorable cases. However, its great utility implies an increase in the difficulty of the tools used, mostly based on homological algebra. In our case, Serre’s spectral sequence allows us to relate the homology (or cohomology) groups of the base, fiber, and total space of a fibration, under some hypotheses about the structure of the base. Finally, the possibility of building a fibration from any space, called path fibration, will open up a wide range of possibilities for applying Serre’s spectral sequence.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Javier J. Gutiérrez Marín

Citation

Citation

BISBAL CASTAÑER, Onofre. La successió espectral de Serre i algunes aplicacions. [consulted: 13 of August of 2026]. Available at: https://hdl.handle.net/2445/198338

Export metadata

JSON - METS

Share record