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Complexification of Lambda Length as Parameter for SL(2, C) Representation Space of Punctured Surface Groups
Author(s) -
Nakanishi Toshihiro,
Näätänen Marjatta
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610704005435
Subject(s) - complexification , representation (politics) , space (punctuation) , surface (topology) , mathematics , lambda , group (periodic table) , class (philosophy) , pure mathematics , geometry , combinatorics , mathematical analysis , algebra over a field , physics , computer science , optics , artificial intelligence , quantum mechanics , politics , political science , law , operating system
A coordinate‐system called λ‐lengths is constructed for an SL(2, C) representation space of punctured surface groups. These λ‐lengths can be considered as complexification of R. C. Penner's λ‐lengths for decorated Teichmüller spaces of punctured surfaces. Via the coordinates the mapping class group acts on the representation space as a group of rational transformations. This fact is applied to find hyperbolic 3‐manifolds which fibre over the circle.