What is a ribbon graph? What is the ribbon graph decomposition of the moduli space of curves? What are some good references for this material?



Ribbon graph decomposition of the moduli space of curves
There are a number of essentially different ways to get coordinates on moduli space using ribbon graphs. The survey


MR0963064 (90a:32026)
Harer, John L.
The cohomology of the moduli space of curves. Theory of moduli (Montecatini Terme, 1985), 138--221,
Lecture Notes in Math., 1337, Springer, Berlin, 1988.


by Harer gives an inspiring account of one of them. Another useful survey is the article "Lambda Lengths" by Penner, which can be downloaded at the bottom of the following webpage : 


<http://www.ctqm.au.dk/events/2006/August/>


Penner is doing something slightly different (his spaces have certain decorations), but it is still quite useful.


