Traces in complex hyperbolic geometry
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Date
2015-11-16
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Abstract
This thesis concerns the study of traces in complex hyperbolic geometry. In this
thesis we review a paper by Parker. We begin by looking at basic notions of
complex hyperbolic geometry, specifically for the complex hyperbolic space. The
main results of the thesis fall into three broad chapters. In the third chapter we
reconstruct the proof of proposition We prove that A has a unique fixed point in H2 C
corresponding to one of the eigenspaces. We also amplify calculations given
by Parker. Finally we discuss the merits on the two
ways to parametrise pair of pants groups. As an application, we compute traces
of matrices generated by complex reflections in the sides of complex hyperbolic
triangle groups in the fifth chapter.
Description
A thesis submitted to the Department of Mathematics,
Kwame Nkrumah University of Science and Technology in
partial fulfillment of the requirement for the Degree
of Master of Philosophy in Pure Mathematics, 2015