On the Lego-Teichmuller game

Bojko Bakalov; Alexander Kirillov

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On the Lego-Teichmuller game

Bojko Bakalov·Alexander Kirillov

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Abstract

For a smooth oriented surface S, denote by M(S) the set of all ways to represent S as a result of gluing together standard spheres with holes (``the Lego game''). In this paper we give a full set of simple moves and relations which turn M(S) into a connected and simply-connected 2-complex. Results of this kind were first obtained by Moore and Seiberg, but their paper contains serious gaps. Our proof is based on a different approach and is much more rigorous.

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Bojko Bakalov, Alexander Kirillov. 1998-09-10. On the Lego-Teichmuller game. https://arxiv.org/abs/math/9809057

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