Labeled double pants decompositions

Anna Felikson^ab, Sergey Natanzon<sup>cdef

a</sup> Independent University of Moscow, Moscow, Russia
^b Jacobs University Bremen, School of Engineering and Science, Bremen, Germany
^c Higher School of Economics, Faculty of Mathematics, Moscow, Russia
^d Belozersky Institute of Physico-Chemical Biology, Moscow State University
^e Institute Theoretical and Experimental Physics
^f Laboratory of Geometrical Methods of Mathematical Physics, MSU

Abstract: A double pants decomposition of a 2-dimensional surface is a collection of two pants decomposition of this surface introduced in [3]. There are two natural operations acting on double pants decompositions: flips and handle-twists. It is shown in [3] that the groupoid generated by flips and handle-twists acts transitively on admissible double pants decompositions where the class of admissible decompositions has a natural topological and combinatorial description. In this paper, we label the curves of double pants decompositions and show that for all but one surfaces the same groupoid acts transitively on all labeled admissible double pants decompositions. The only exclusion is a sphere with two handles, where the groupoid has 15 orbits.

Key words and phrases: pants decomposition, mapping class group.

MSC: 57M50

Received: September 13, 2010

Language: English

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