Moscow Mathematical Journal

Volume 17, Issue 1, January–March 2017 pp. 51–58.

Double Pants Decompositions Revisited

Authors: Anna Felikson (1) and Sergey Natanzon (2)
Author institution:(1) Department of Mathematical Sciences, Durham University, Science Laboratories, South Road, Durham, DH1 3LE, UK
(2) National Research University Higher School of Economics (HSE), 20 Myasnitskaya ulitsa, Moscow 101000, Russia;
Institute for Theoretical and Experimental Physics (ITEP), 25 B. Cheremushkinskaya, Moscow 117218, Russia

Summary:

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.

2010 Math. Subj. Class. 57M50.

Keywords: Pants decomposition, Heegaard splitting, curve complex.

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