On the lego-teichmüller game

B. Bakalov; A. Kirillov

doi:10.1007/BF01679714

On the lego-teichmüller game

B. Bakalov
, A. Kirillov

Mathematics

Massachusetts Institute of Technology

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

For a smooth oriented surface Σ, denote by M(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 turn M(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.

Original language	English
Pages (from-to)	207-244
Number of pages	38
Journal	Transformation Groups
Volume	5
Issue number	3
DOIs	https://doi.org/10.1007/BF01679714
State	Published - 2000

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abstract = "For a smooth oriented surface Σ, denote by M(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 turn M(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.",

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AU - Kirillov, A.

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N2 - For a smooth oriented surface Σ, denote by M(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 turn M(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.

AB - For a smooth oriented surface Σ, denote by M(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 turn M(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.

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DO - 10.1007/BF01679714

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SN - 1083-4362

VL - 5

SP - 207

EP - 244

JO - Transformation Groups

JF - Transformation Groups

IS - 3

ER -

On the lego-teichmüller game

Abstract

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