- Title Information
- Title
- On the Algebraic Aspects of Complex Hyperbolic Triangle Groups
- Name:
Personal
- Name Part
- Wang, Yuhan
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Schwartz, Richard
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Goodwille, Thomas
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Kahn, Jeremy
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2020
- Physical Description
- Extent
- x, 51 p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2020
- Genre (aat)
- theses
- Abstract
- A $(p,q,r)$-complex hyperbolic triangle group is a group generated by complex reflections across complex geodesics meeting at angles $\pi/p, \pi/q, \pi/r$. In this thesis, we study the algebraic aspects of complex hyperbolic triangle groups and answer questions related to their discreteness. In part I, we classify all complex hyperbolic triangle groups by types. The type of a complex hyperbolic triangle group is defined according to the ellipticity of the two words $I_1I_3I_2I_3$ and $I_1I_2I_3$. Algebraically, the type is decided by which trace of the words would enter the deltoid first. We use algebraic technique to show directly the type is determined by a particular polynomial in the cosines of the angles with integer coefficients. In part II, we study $(p,q,r;n)$-triangle groups, which are $(p,q,r)$-triangle groups with the additional constraint $I_1I_3I_2I_3$ has order $n$. In particular, we use algebraic techniques developed in Part I to show that for a discrete $(p,q,r;n)$-triangle group with $p>22$, $I_1I_2I_3$ must be finite-order regular elliptic.
- Subject
- Topic
- complex hyperbolic geomtry
- Subject
- Topic
- triangle groups
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00894972")
- Topic
- Discrete groups
- Subject
- Topic
- PU(2,1) representations
- Subject
- Topic
- complex hyperbolic triangle groups
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20200720
- Access Condition:
rights statement
(href="http://rightsstatements.org/vocab/InC/1.0/")
- In Copyright
- Access Condition:
restriction on access
- Collection is open for research.
- Identifier:
DOI
- 10.26300/8q55-ck20
- Type of Resource (primo)
- dissertations