[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2014.51.2.403

INVOLUTIONS AND THE FRICKE SPACES OF SURFACES WITH BOUNDARY

Kim, Hong Chan (Department of Mathematics Education Korea University)

Publication Information

Journal of the Korean Mathematical Society / v.51, no.2, 2014 , pp. 403-426 More about this Journal

Abstract

The purpose of this paper is to find expressions of the Fricke spaces of some basic surfaces which are a three-holed sphere ${\sum}$ (0, 3), a one-holed torus ${\sum}$ (1, 1), and a four-holed sphere ${\sum}$ (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, $\mathbb{C}$ ) to SL(2, $\mathbb{C}$ ), play a very important role in determining the discreteness of holonomy groups.

Keywords

Fricke space; involution; discrete holonomy group;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
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