Supervisors info:
Ιωάννης Εμμανουήλ, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ, (Επιβλέπων)
Κοντογεώργης Αριστείδης, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Ντόκας Ιωάννης, Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Summary:
In homological algebra and in algebraic topology spectral sequences are an
important tool for the computation of homology and cohomology groups.
Jean Leray working on problems in algebraic topology defined the notion
of a sheaf and in order to calculate the cohomology of sheafs created a
computational tool now known as the Leray spectral sequence. The math
ematical community soon realized that this techinque was part of a much
broader phenomenon. This realization led to the development of the theory
of spectral sequences. In this dissertation we will introduce some of the
basic notions and results of the theory of spectral sequences. In the final
chapter we will see some applications of spectral sequences namely we will
use the Hochschild-Serre spectral sequence to compute the homology and
cohomology groups of some Lie algebras.
