Abstract
This chapter has two main purposes; the first is to classify function groups up to similarity, and regular (i.e., geometrically finite) function groups up to deformation, and the second is to show that every regular covering of a finite Riemann surface, where the covering surface is planar, can be topologically realized by a regular function group. Using similar techniques with quasiconformal mappings, one can prove that every planar regular covering of a finite Riemann surface can be conformally realized by a regular function group; this theorem however is beyond the scope of this book.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Maskit, B. (1988). Function Groups. In: Kleinian Groups. Grundlehren der mathematischen Wissenschaften, vol 287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61590-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-61590-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64878-6
Online ISBN: 978-3-642-61590-0
eBook Packages: Springer Book Archive