Transformation Groups

, Volume 5, Issue 3, pp 207–244

On the Lego-Teichmüller game

  • B. Bakalov
  • A. KirillovJr.

DOI: 10.1007/BF01679714

Cite this article as:
Bakalov, B. & Kirillov, A. Transformation Groups (2000) 5: 207. doi:10.1007/BF01679714


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.

Copyright information

© Birkhäuser Boston 2000

Authors and Affiliations

  • B. Bakalov
    • 1
  • A. KirillovJr.
    • 2
  1. 1.Department of MathematicsMITCambridgeUSA
  2. 2.Department of MathematicsSUNY at Stony BrookStony BrookUSA