Spanning disks for domains with free fundamental groups
نویسندگان
چکیده
منابع مشابه
Computing fundamental domains for Fuchsian groups par
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...
متن کاملComputing Fundamental Domains for Fuchsian Groups
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...
متن کاملFundamental domains for lattices in rank one semisimple lie groups.
We construct a fundamental domain omega for an arbitrary lattice [unk] in a real rank one, real simple Lie group, where omega has finitely many cusps (i.e., is a finite union of Siegel sets) and has the Siegel property (i.e., the set {gamma [unk] [unk]|omegagamma [unk] omega [unk] varphi} is finite). From the existence of omega we derive a number of consequences. In particular, we show that [un...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1977
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-38-1-69-72