A deformation of Penner's simplicial coordinate

Abstract: We produce a one-parameter family of coordinates

{P s i_{h}}_{h i n m a t h b b R}

of the decorated Teichm"{u}ller space of an ideally triangulated punctured surface

(S, T)

with negative Euler characteristic, which is a deformation of Penner's simplicial coordinate cite{P1}. If

h g e q s l a n t 0

, the decorated Teichm"{u}ller space in the

P s i_{h}

coordinate becomes an explicit convex polytope

P (T)

independent of

h

, and if

h < 0

, the decorated Teichm"{u}ller space becomes an explicit bounded convex polytope

P_{h} (T)

so that

P_{h} (T) s u b s e t P_{h^{'}} (T)

if

h < h^{'}

. As a consequence, Bowditch-Epstein and Penner's cell decomposition of the decorated Teichm"{u}ller space is reproduced.

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