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
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.
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- The London Mathematical Society 2004
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