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Deformation theory and finite simple quotients of triangle groups II
- Source :
- Groups, Geometry, and Dynamics
- Publication Year :
- 2014
- Publisher :
- European Mathematical Society - EMS - Publishing House GmbH, 2014.
-
Abstract
- Let $2 \leq a \leq b \leq c \in \mathbb{N}$ with $��=1/a+1/b+1/c$ be the corresponding hyperbolic triangle group. Many papers have been dedicated to the following question: what are the finite (simple) groups which appear as quotients of $T$? (Classically, for $(a,b,c)=(2,3,7)$ and more recently also for general $(a,b,c)$.) These papers have used either explicit constructive methods or probabilistic ones. The goal of this paper is to present a new approach based on the theory of representation varieties (via deformation theory). As a corollary we essentially prove a conjecture of Marion [21] showing that various finite simple groups are not quotients of $T$, as well as positive results showing that many finite simple groups are quotients of $T$.
- Subjects :
- Pure mathematics
General Mathematics
Deformation theory
Group Theory (math.GR)
01 natural sciences
Combinatorics
Group of Lie type
Simple (abstract algebra)
0103 physical sciences
FOS: Mathematics
Discrete Mathematics and Combinatorics
Schwarz triangle
0101 mathematics
Quotient
Mathematics
Conjecture
Group (mathematics)
Applied Mathematics
010102 general mathematics
Algebra
Simple group
Homomorphism
010307 mathematical physics
Geometry and Topology
Classification of finite simple groups
Triangle group
Mathematics - Group Theory
Hyperbolic triangle
Group theory
Subjects
Details
- ISSN :
- 16617207
- Volume :
- 8
- Database :
- OpenAIRE
- Journal :
- Groups, Geometry, and Dynamics
- Accession number :
- edsair.doi.dedup.....4d64e900647ee4d0aefb26739af26b0f