Abstract :

Spectral Sequences are one of the most useful tools in topology to relate the homology, cohomology groups of various spaces. For instance, Given a pair $(X,A)$ of topological spaces, one can often relate the homology, cohomology groups of $X$ and $A$ with the help of associated long exact sequence. Instead of taking $A\subset X$ one can consider any arbitrary filtration $X_0\subset X_1\subset\ldots\subset X$ of $X$ and then gets the associated homology and cohomology spectral sequence. The goal of the talk will be to discuss the general setting with sequences of groups and differentials and then analyzing from the topological point of view with the groups as associated homology or cohomology groups.