Analytic Families of Homomorphisms into PSL(2, C)

作者：Mejia Diego^*; Pommerenke Christian

来源：Computational Methods and Function Theory, 2010, 10(1): 81-96.

DOI：10.1007/BF03321756

• Analytic family
• homomorphism
• Kleinian group
• singular set
• Moebius transformation
• trace
• non-elementary group

We develop a systematic theory of families of homomorphisms
h(t) : G -> PSL(2, C), t is an element of T,
that depend analytically on the complex parameter t. Important results have been obtained by Jorgensen, Riley and Sullivan.
The main new concept is the singular set S of parameter values t for which some Moebius transformation h(t)(x) becomes non-loxodromic. We study the structure and geometry of S and the behaviour of ht in domains V subset of T \ (S) over bar, in particular the extension to values in partial derivative V boolean AND partial derivative T.

• 出版日期2010