Silvia Benvenuti, Riccardo Piergallini
Published 2007-10-08, updated 2007-10-27Version 2
We exhibit a set of edges (moves) and 2-cells (relations) making the complex of pant decompositions on a surface a simply connected complex. Our construction, unlike the previous ones, keeps the arguments concerning the structural transformations independent from those deriving from the action of the mapping class group. The moves and the relations turn out to be supported in subsurfaces with 3g-3+n=1,2 (where g is the genus and n is the number of boundary components), illustrating in this way the so called Grothendieck principle.
Comments: Minor changes in the introduction
A lower bound of the distortion of the Torelli group in the mapping class group with boundary components
The abelianization of the level 2 mapping class group
Mapping class groups of surfaces of genus $\geq 3$ do not virtually surject to $\mathbb{Z}$
![QR code for arXiv:0710.1483 [math.GT]](http://oss.arxitics.com/images/favicon.svg)