fractionally coloring the plane

The fractional chromatic number of the plane is at least 105/29

We actually wrote down the proof for 76/21, but at the end of section 3 we show how to improve this to 105/29, it complicates the discharging with a few more phases.  This is the limit of our method because any larger value and we can't prove that a maximum weight independent set has to intersect the core in a maximal independent set in the triangular lattice.

Here are the pretty pictures.