Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T06:24:32.294Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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