Fundamental domains for properly discontinuous affine groups
نویسندگان
چکیده
منابع مشابه
Properly discontinuous groups on certain matrix homogeneous spaces
We characterize discrete groups Γ ⊂ GL(n,R) which act properly discontinuously on the homogeneous space GL(m,R)\GL(n,R).
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We exhibit an algorithm to compute a Dirichlet domain for a Fuchsian group Γ with cofinite area. As a consequence, we compute the invariants of Γ, including an explicit finite presentation for Γ. Let Γ ⊂ PSL2(R) be a Fuchsian group, a discrete group of orientationpreserving isometries of the upper half-plane H with hyperbolic metric d. A fundamental domain for Γ is a closed domain D ⊂ H such th...
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We exhibit an algorithm to compute a Dirichlet domain for a Fuchsian group Γ with cofinite area. As a consequence, we compute the invariants of Γ, including an explicit finite presentation for Γ. Let Γ ⊂ PSL2(R) be a Fuchsian group, a discrete group of orientationpreserving isometries of the upper half-plane H with hyperbolic metric d. A fundamental domain for Γ is a closed domain D ⊂ H such th...
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Let K be a totally real algebraic number field and O an order in a quaternion algebra A over K. Assume that the group O1 of units in O with reduced norm equal to 1 is embedded into PSL2(R) as an arithmetic Fuchsian group. It is shown how Ford’s algorithm can be effectively applied in order to determine a fundamental domain of O1 as well as a complete system of generators of O1.
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The moduli space QMg of genus g quadratic differentials has a natural action of G = GL2 (R)/ 〈± ( 1 0 0 1 )〉 and the Veech group PSL(X, q) is the stabilizer of (X, q) ∈ QMg in G. We describe a new algorithm for finding elements of PSL(X, q) which, for lattice Veech groups, can be used to compute a fundamental domain and generators. Using our algorithm, we give the first explicit examples of gen...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2013
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-013-9895-5