, Volume 5, Issue 3, pp 207-244

On the Lego-Teichmüller game

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Abstract

For a smooth oriented surface Σ, denote byM(Σ) the set of all ways to represent Σ 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 turnM(Σ) 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.

Supported in part by NSF Grant DMS9622870.
Supported in part by NSF Grant DMS9610201.