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The bar construction is a way to turn an algebraic object into a topological space.

References: 

• Two sided Bar construction: http://math.stanford.edu/~carym/bar.pdf
• General Orbifold constructions: Adem, Leida & Ruan - Orbifolds and Stringy Topology

 

Background.

In this post I'll introduce group homology and cohomology. The main reference for this entry will be Kenneth Brown's 'Cohomology of Groups'.

Over the last year spectral sequences seem to be being mentioned more and more, so I figured it was probably about time I worked out sort of what they're all about. I won't give the most generic definitions, I'll more aim to give an idea of how they work and then have a look at the Serre Spectral Sequence.