Two-generator discrete subgroups of \(\text{Isom}(\mathbb{H}^2)\) containing orientation-reversing elements

DOI10.1023/A:1005032526329zbMath0928.20040OpenAlexW16908151MaRDI QIDQ1275311

Elena Klimenko, Makoto Sakuma

Publication date: 31 October 1999

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1005032526329

zbMATH Keywords

Montesinos knots2-generator discrete subgroupsextended triangle groupsorientation-reversing elementstunnel numbers

Mathematics Subject Classification ID

Topological methods in group theory (57M07) Discrete subgroups of Lie groups (22E40) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Discontinuous groups of transformations (57S30) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35) Reflection groups, reflection geometries (51F15)

Related Items (13)

ON DOUBLE-TORUS KNOTS (II) ⋮ ALL DISCRETE $\mathcal{RP}$ GROUPS WHOSE GENERATORS HAVE REAL TRACES ⋮ Euclidean simplices generating discrete reflection groups ⋮ Double branched covers of tunnel number one knots ⋮ Ribbon \(2\)-knot groups of Coxeter type ⋮ A two-dimensional slice through the parameter space of two-generator Kleinian groups ⋮ Census of the Complex Hyperbolic Sporadic Triangle Groups ⋮ Discreteness criteria for \(\mathcal{RP}\) groups ⋮ Unnamed Item ⋮ Reflection subgroups of Coxeter groups ⋮ The topology, geometry and algebra of unknotting tunnels ⋮ Knot Floer homology of \((1,1)\)-knots ⋮ Morimoto--Sakuma--Yokota's geometric approach to tunnel number one knots

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