Pants Decompositions of Surfaces
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Randich, Joseph
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Abstract
In this Master Thesis, we consider pants decompositions of any orientable 2-dimensional surface with any genus <i>g</i>. We show that any decomposition compatible with the same zipper system, and which is contractible in the inner handlebody corresponding to the decomposition, may be transformed into any other decomposition satisfying the same conditions via elementary transformations known as zipped flips. This puts us one step closer to showing that the groupoid on double pants decompositions, introduced by Felikson and Natanzon in [5], acts transitively on its objects.