A commutative braid of exact sequences
To start things off, here is what the whiteboard in my office currently looks like. This beautiful diagram was drawn by Patrick Orson and it represents many different sequences of topological spaces. The sequences are interwoven so as to form an object called a commutative braid.

Aha. This now explain why Andrew was asking me a few days ago about an explicit geometric realisation of BSO(3)! :)
June 22, 2011 at 11:21 am
Beautiful! I have so much to learn still, it’s daunting at times.
June 24, 2011 at 3:42 pm
My 2009 Dublin lecture http://www.maths.ed.ac.uk/~aar/slides/lewis.pdf has many examples of braids, mathematical and otherwise!
July 20, 2011 at 7:31 pm