Show your mathematics to the world!

Cayley graph

Cayley group of F_2Our photo this week is by Christian Perfect, a PhD student at the University of Newcastle. He was drawing a Cayley graph, which is a picture encoding the structure of a group. This particular picture is a drawing of the structure of F2, the free group on two generators. This group is generated by the elements {x,y,x-1, y-1} with x and x-1 being right and left arrows, and y and y-1 being up and down arrows respectively. Each element of the group is then a vertex of the graph. For example, to find the vertex corresponding to xyx2y-1 you start in the middle and go right, up, right, right, down.

This picture can also be interpreted (if you are a topologist!) as the universal cover of the ‘8’, or infinity, symbol.

Christian actually took a series of photos as he was drawing the graph. I’ve put these together into an animated gif for your viewing pleasure (but beware – it’s 30Mb!).

Advertisements

One response

  1. There is a thickened Cayley graph on the blackboard in the photo of Des Sheiham in http://www.maths.ed.ac.uk/~aar/des.htm

    August 8, 2011 at 9:23 pm

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s