Katok S. — Fuchsian Groups :: Электронная библиотека попечительского совета мехмата МГУ

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Katok S. — Fuchsian Groups

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Название: Fuchsian Groups

Автор: Katok S.

Аннотация:

This introductory text provides a thoroughly modern treatment of Fuchsian groups that addresses both the classical material and recent developments in the field. A basic example of lattices in semisimple groups, Fuchsian groups have extensive connections to the theory of a single complex variable, number theory, algebraic and differential geometry, topology, Lie theory, representation theory, and group theory.

Язык:

Рубрика: Математика/Алгебра/Теория групп/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 175

Добавлена в каталог: 26.03.2005

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Предметный указатель

      see Centralizer
      36 see
$\Gamma(A,\sigma)$       119
$\Gamma\H$       75 see
$\hat{C}$       8see Riemann sphere)
$\Lambda(\Gamma)$       33 see
$\mathcal{O}$       118 see
$\mu(\Gamma\H)$       75 see
$\Sigma$       8 see Euclidean
$\varphi(n)$       138 see
Algebraically closed field      115
angle      10
Angle of parallelism      15
C      1see Complex plane
Cauchy — Riemann equations      12 157
Centralizer (of an element g in a group G)      34 see
Commensurable groups      120
Complex plane      1 see
Cosine Rule I      16
Cosine Rule II      16
Cross-ratio      6
Division algebra      113see Skew-field
Euler function      138 see $\varphi(n)$
Example $C\Gamma_8)$       95 148
Example A $(PSL(2,\mathbb{Z}))$       29 34 55 71 74 75
Example B $(z \to 2z)$       33 49
Example E $(H = (\frak{-1, -1}{\mathbb{R}}))$       118 124
Example F $(\Gamma(2))$       141
Example G $((\frak{3, 5}{Q}))$       143
Example H $(\Gamma(2 cos \frak{\pi}{m}))$       150
Fractional linear transformation      2 see PSL(2
Fuchsian group      26
Fuchsian group of the first kind      67
Fuchsian group of the second kind      67
Fuchsian group, arithmetic      112 120
Fuchsian group, cocompact      84
Fuchsian group, congruent points with respect to      70
Fuchsian group, derived from a quaternion algebra      120
Fuchsian group, Dirichlet region for      52
Fuchsian group, Dirichlet region for, boundary of      49 80
Fuchsian group, Dirichlet region for, congruent sides of      73
Fuchsian group, Dirichlet region for, cycle of      70
Fuchsian group, Dirichlet region for, elliptic cycle of      70
Fuchsian group, Dirichlet region for, elliptic vertex of      70
Fuchsian group, Dirichlet region for, Euclidean boundary of      80
Fuchsian group, Dirichlet region for, Euclidean closure of      80
Fuchsian group, Dirichlet region for, extended set of vertices of      70
Fuchsian group, Dirichlet region for, free side of      80
Fuchsian group, Dirichlet region for, side of      70
Fuchsian group, Dirichlet region for, vertex at infinity of      72
Fuchsian group, Dirichlet region for, vertex of      67
Fuchsian group, elementary      37
Fuchsian group, Ford fundamental region for      61
Fuchsian group, fundamental region for      49
Fuchsian group, fundamental region for, locally finite, geometrically finite      80
Fuchsian group, limit set of      33 63 see
Fuchsian group, maximal cyclic parabolic subgroup of      72
Fuchsian group, maximal cyclic parabolic subgroup of, conjugacy classes of      72 see
Fuchsian group, maximal finite cyclic subgroup of      71
Fuchsian group, maximal finite cyclic subgroup of, conjugacy classes of      71
Fuchsian group, parabolic class number of      72 139
Fuchsian group, periods of      71
Fuchsian group, quotient space of      75 see
Fuchsian group, quotient space of, cusp of      75 139
Fuchsian group, quotient space of, marked point of      75
Fuchsian group, signature of      91
Fuchsian group, triangle group      99
F[x]      115 see
Gauss — Bonnet formula      13
Genus (of a surface)      75
Geodesic in H      1
Geodesic- in U      8
H      113 see
H (Hamiltonian quaternion algebra)      113 see
Hecke group      151 see
Horocycle      87
Hyperbolic area in H      11
Hyperbolic area of $\Gamma\H$       75 see
Hyperbolic distance in H      2
Hyperbolic distance in H, formulae for      6—7
Hyperbolic distance in U, formulae for      21
Hyperbolic length in H      1
Hyperbolic metric in H      1
Hyperbolic metric in U      7
Hyperbolic plane      1 see
Hyperbolic plane, Euclidean boundary of      8
Hyperbolic plane, Euclidean closure of      8
Hyperbolic plane, model of in H      1
Hyperbolic plane, model of in U      7

Hyperbolic plane, points at infinity of      8
Hyperbolic polygon      12
Hyperbolic reflection      99
Hyperbolic triangle      12
Hyperbolic trigonometry      15
Hyperbolically convex region      54
id      3 see
Infinity, $\infty$       6
Inverse points      59
Inversion in a circle      58
Isom(H)      4 see
Isom(H), discrete subgroup of      26
Isometric circle      56
Isometry      3
Isometry, anti-conformal      10
Isometry, conformal      10
Isometry, orientation of      10
Isometry, orientation-preserving      10
Isometry, orientation-reversing      10
Isomorphic, $\approx$ (groups, quaternion algebras, fields)      3 113 114
Jacobian      12
Jorgensen inequality      41
Locally finite family      27
Metric space, group of homeomorphisms of      27
Metric space, group of homeomorphisms of, acting properly discontinuously on      27
Metric space, group of homeomorphisms of, acting properly discontinuously on, fundamental region for      49
Metric space, group of homeomorphisms of, acting properly discontinuously on, fundamental region for, boundary of a fundamental region F, $\partial F$       49
Metric space, tessellation of      49
Minkowski's Lemma      129
Mobius transformation      2 see
Modular group      29 see Example
Modular group, principal congruence subgroup of level n in      133
Non-Euclidean geometry      1
Normalizer (of a subgroup H in a group G)      36 see
Orbifold      75
Orbit (of a group G, G-orbit)      27
Ordinary point      63
Perpendicular bisector      53
Poincare's theorem      92
Principal circle      8 see Euclidean
PS*L(2,R)      8 see
PSL(2,R)      3 see Mobius
PSL(2,R), conjugate elements in      35
PSL(2,R), elliptic element of      23
PSL(2,R), elliptic element of, fixed point of      23
PSL(2,R), hyperbolic element of      23
PSL(2,R), hyperbolic element of, axis of      24
PSL(2,R), hyperbolic element of, fixed points (repulsive and attractive) of      23
PSL(2,R), identity element in      3 see
PSL(2,R), norm of an element      25—26
PSL(2,R), parabolic element of      23
PSL(2,R), parabolic element of, fixed point of      23
PSL(2,R), trace of an element      3 23
PSL(2,Z)      29 see Example
Pythagorian Theorem      18
Quadratic non-residue      116
Quaternion algebra      113
Quaternion algebra, center of      113
Quaternion algebra, order in      118 see
Quaternion algebra, order in, group of units in 0 of reduced norm 1      119
Quaternion algebra, radical of      113
Quaternion algebra, ramified at a place      117
Quaternion algebra, reduced norm of an element in      115
Quaternion algebra, reduced trace of an element in      115
Quaternion algebra, standard involution in      115
Quaternion algebra, unramified at a place      117
Riemann sphere      6 see
Riemann surface      76
Ring of polynomials over a field F      115 see
S*L(2,R)      8
Siegel's theorem      80
Simple central algebra      113
Sine rule      16
Skew-field      113 see
SL(2,R), identity matrix in,       3
Sphere of imaginary radius      18
Spherical triangle      19
Totally real algebraic number field      117
Triangle inequality      2
U      7 see
Unimodular group      2 see
Unit disc      1 see
Unit disc, Euclidean boundary of      8 see Principal
Unit disc, Euclidean closure of      8
Upper half-plane      1 see
Upper half-plane, Dirichlet tessellation of      74
Upper half-plane, Dirichlet tessellation of, face of      74
Upper half-plane, Euclidean boundary of      8
Upper half-plane, Euclidean closure of      8

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