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Apr 7, 2012 at 10:06 comment added Ryan Budney Provided $g \geq 2$ such a maximal collection is called a pant decomposition of the surface. That there's $3g-3$ curves in such a decomposition is a very old result, observed probably by many people but certainly well-known by Poincare's time. Such curve collections are used to put "coordinates" on the collection of all curves on the surface, usually called "Dehn-Thurston coordinates".
Apr 7, 2012 at 9:52 comment added Sam Nead You should google "pants decomposition". Here is one hit. brownsharpie.courtneygibbons.org/?p=144
Apr 6, 2012 at 15:26 answer added eigenbunny timeline score: 1
Apr 6, 2012 at 14:49 vote accept CommunityBot
Apr 6, 2012 at 14:31 answer added Tony Huynh timeline score: 1
Apr 6, 2012 at 14:19 history asked user13946 CC BY-SA 3.0