Double pants decompositions revisited

Anna Felikson^a, Sergey Natanzon<sup>bc

a</sup> Department of Mathematical Sciences, Durham University, Science Laboratories, South Road, Durham, DH1 3LE, UK
^b National Research University Higher School of Economics (HSE), 20 Myasnitskaya ulitsa, Moscow 101000, Russia
^c Institute for Theoretical and Experimental Physics (ITEP), 25 B. Cheremushkinskaya, Moscow 117218, Russia

Abstract: Double pants decompositions were introduced by the authors in 2011, together with a flip-twist groupoid acting on these decompositions. It was shown that flip-twist groupoid acts transitively on a certain topological class of the decompositions, however, recently Randich discovered a serious mistake in the proof. In this note we present a new proof of the result, accessible without reading the initial paper.

Key words and phrases: pants decomposition, Heegaard splitting, curve complex.

MSC: 57M50

Received: October 6, 2015; in revised form November 30, 2016

Language: English

DOI: 10.17323/1609-4514-2017-17-1-51-58

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