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COMPLEXIFICATION OF LAMBDA LENGTH AS PARAMETER FOR SL$(2,{\Bbb C})$ REPRESENTATION SPACE OF PUNCTURED SURFACE GROUPS

Published online by Cambridge University Press:  01 October 2004

TOSHIHIRO NAKANISHI  and
MARJATTA NÄÄTÄNEN
TOSHIHIRO NAKANISHI
Affiliation:
Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japantosihiro@math.nagoya-u.ac.jp Current address:, Department of Mathematics, Shimane University, Matsue 690-8504, Japantosihiro@math.shimane-u.ac.jp
MARJATTA NÄÄTÄNEN
Affiliation:
Department of Mathematics, PL 4 (Yliopistonkatu 5), 00014 University of Helsinki, Finlandmarjatta.naatanen@helsinki.fi
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Abstract

A coordinate-system called $\lambda$-lengths is constructed for an SL$(2,{\Bbb C})$ representation space of punctured surface groups. These $\lambda$-lengths can be considered as complexification of R. C. Penner's $\lambda$-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.

Keywords

30F40 (primary)57M05 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 70 , Issue 2 , October 2004 , pp. 383 - 404
Copyright
The London Mathematical Society 2004

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Footnotes

Partially supported by Grant-in-Aid for Scientific Research (13440045), Ministry of Education, Science and Culture of Japan.