Toshihiro Nakanishi

Complexification of lambda length as parameter for SL(2,C) representation space of punctured surface groups


We intoroduce coordinates to an $SL(2,{¥Bf C})$-representation space of a punctured surface group, which can be regarded as a complexification of the $¥lambda$ lengths introduced by R. C. Penner to his decorated Teichm¥"uller space. Via the coordinates, the mapping class group acts on the representation space as a group of rational transformations. We can apply this fact to find hyperbolic $3$-manifolds fibered over the circle with fibers a puncuted surface.

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