INVOLUTIONS AND THE FRICKE SPACES OF SURFACES WITH BOUNDARY

Title & Authors
INVOLUTIONS AND THE FRICKE SPACES OF SURFACES WITH BOUNDARY
Kim, Hong Chan;

Abstract
The purpose of this paper is to find expressions of the Fricke spaces of some basic surfaces which are a three-holed sphere $\small{{\sum}}$(0, 3), a one-holed torus $\small{{\sum}}$(1, 1), and a four-holed sphere $\small{{\sum}}$(0, 4). For this goal, we define the involutions corresponding to oriented axes of loxodromic elements and an inner product <,> which gives the information about locations of axes of loxodromic elements. The signs of traces of holonomy elements, which are calculated by lifting a representation from PSL(2, $\small{\mathbb{C}}$) to SL(2, $\small{\mathbb{C}}$), play a very important role in determining the discreteness of holonomy groups.
Keywords
Fricke space;involution;discrete holonomy group;
Language
English
Cited by
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