The Riley slice revisited
The Riley slice revisited
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重新审视莱利切片
DOI：
10.2140/gtm.1998.1.303
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
C. Series
中科院分区：
文献类型：
--
作者：
Y. Komori;C. Series
In [4], Keen and Series analysed the theory of pleating coordinates in the context of the Riley slice of Schottky space R, the deformation space of a genus two handlebody generated by two parabolics. This theory aims to give a complete description of the deformation space of a holomorphic family of Kleinian groups in terms of the bending lamination of the convex hull boundary of the associated three manifold. In this note, we review the present status of the theory and discuss more carefully than in [4] the enumeration of the possible bending laminations for R, complicated in this case by the fact that the associated three manifold has compressible boundary. We correct two complementary errors in [4], which arose from subtleties of the enumeration, in particular showing that, contrary to the assertion made in [4], the pleating rays, namely the loci in R in which the projective measure class of the bending lamination is fixed, have two connected components. AMS Classification 30F40; 32G05
