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Thurston W.P. — The Geometry and Topology of Three-Manifolds
Thurston W.P. — The Geometry and Topology of Three-Manifolds

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Название: The Geometry and Topology of Three-Manifolds

Автор: Thurston W.P.

Аннотация:

This is an electronic edition of the 1980 lecture notes distributed by Princeton University. The text was typed in TeX by Sheila Newbery, who also scanned the figures. Typos have been corrected (and probably others introduced), but otherwise no attempt has been made to update the contents. Genevieve Walsh compiled the index.
Numbers on the right margin correspond to the original edition's page numbers.

Thurston's Three-Dimensional Geometry and Topology, Volume 1 (Princeton University Press, 1997) is a considerable expansion of the first few chapters of these notes. Later chapters have not yet appeared in book form.


Язык: en

Рубрика: Математика/Геометрия и топология/Алгебраическая и дифференциальная топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 360

Добавлена в каталог: 23.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$M_{\Gamma}$      179
$N_{\Gamma}$      180
$O_{\Gamma}$      180
$PSL(2,\mathbb{C})$      92—96
$P_{\Gamma}$      180
$\mathcal{GL}(S)$      209 215
$\mathcal{G}$-manifold      27
$\mathcal{G}$-orbifold      301
$\mathcal{H}$-foliation      see “Foliation”
$\mathcal{ML}(S)$      209 210 251
$\mathcal{ML}_0(S)$      209 251
$\mathcal{N}(O)$      347 351
$\mathcal{PL}(S)$      209
$\mathcal{PL}_0(S)$      210 263
$\mathcal{T}_{\gamma}$      243
(G, X)-manifold      27
Accidental parabolics      257
Action, discrete orbits      175
Action, properly discontinuous      174
Action, wandering      175
Ahlfors’ theorem      180
Algebraic hyperbolic manifolds      168
Algebraic limit      225
Algebraic numbers      143
Andreev’s theorem      330
Bass, H      143
Bending measure      189—191
Bers      111
Billiard table      298
Borromean rings      33—34 105 300 322
Borromean rings, commensurable with Whitehead link      141
Boundary mirror      301
Branched cover over a link      2
Circle packing      330
Circle packing, nerve of      330
Commensurability classes      144
Commensurability classes, infinite number of      150
Commensurable and cusp structure      142
Commensurable with complete manifolds      141
Commensurable, discrete subgroups of $PSL(2,\mathbb{C})$      140
Commensurable, manifolds      140
Complete $\mathcal{H}$-foliation      64
Complete (G,X)-manifold      35
Completeness criteria      36 38 41 42
Completion of a hyperbolic 3-manifold      54—56
Completion of a hyperbolic surface      41—42
Cone manifolds      55—56
Convergence, algebraic      225
Convergence, geometric      225
Convergence, strong      226
Convex      177
Convex hull      171
Convex hull, boundary      185
Convex, locally      177
Convex, locally, implies convex      177
Convex, strictly      178
Convex, strictly and homotopy equivalence      179
Corner reflectors      309
Coxeter diagram      326
Cusp extra      216
Deformations of a 3-manifold      85
Deformations of a 3-manifold, dimension of      88 97
Deformations of a 3-manifold, extend to Dehn filling      103
Deformations of compact convex hyperbolic manifolds      178
Dehn surgery      2 (see
Dehn surgery, invariants      57
Developing map      35 54 185
Developing map of a convex manifold      177
Developing map of a(G,X)-orbifold      309
Developing map of an affine torus      37
Discrete      64
Domain of discontinuity      174
Domain of discontinuity, retraction onto convex hull      174
Edge equations      49—51
Elementary group      171
Elliptic, why distressing      10
Essentially complete      244
Euclidean triangles      47
Euler number for a fibration      323
Extension of a vector field      288
Extension of a vector field, Curl and Div      292
Extension of a vector field, direction derivative of      290
Fibration over an orbifold      319 323
Figure-eight knot      4—7 29—31 120
Figure-eight knot, commensurable with $PSL(2,\mathcal{O}_3)$      149
Figure-eight knot, complete hyperbolic structure      54
Figure-eight knot, Dehn surgery on      58—61 70
Figure-eight knot, Dehn surgery on yields hyperbolic manifold      61
Figure-eight knot, fundamental group      172
Figure-eight knot, gluing diagram      4
Figure-eight knot, incompressible surfaces in      72—83
Figure-eight knot, limit set      172
Figure-eight knot, parametrization space of complement      52
Figure-eight knot, volume of complement      164
Foliation, developing map for      63
Foliation, hyperbolic      62 64
Fricke space      92
Fuchsian group      172 192
Fundamental group, acts ergodically on $S_{\infty}^{n-1}$      111
Gauss — Bonnet for orbifolds      312
Gehring      111
Geodesic flow, conditions for ergodicity      277
Geodesic lamination      186 200 (see see
Geodesic lamination with compact support      239
Geodesic lamination, complete      196
Geodesic lamination, ending      238
Geodesic lamination, essentially complete      243 246
Geodesic lamination, measure on      207
Geodesic lamination, near a cusp      201
Geodesic lamination, realizable      208 211 214 240
Geodesic lamination, realizable, criterion for      261
Geodesic lamination, train track approximation of      204 206 210 213
Geodesics on hyperboloid      18
Geometric limit      225
Geometric structure      85
Geometric topology      225
Geometric topology and compactness      228
Geometric topology on geodesic laminations      208
Geometrically finite      180 183
Geometrically finite, hyperbolic 3-manifold      203
Geometrically finiteand cusps      182
Geometrically near      118
Geometrically tame      219 221 229
Geometrically tame and algebraic convergence      259
Geometrically tame and geodesic flow      278
Geometrically tame, almost      230 240
Geometrically tame, implies topologically tame      240
Gieseking      29
Gromov      102
Gromov’s invariant      123 140
Gromov’s invariant for manifolds with boundary      134
Gromov’s norm      123 127
Gromov’s theorem, relative version      136
Gromov’s theorem, strict version      130
Haken, 3-orbifold      324 325
Haken, manifold      71
Haken, W.      72
Hatcher      101
Heegaard decomposition      3
hilbert      10
Holonomy      35 53 85 97—100
Holonomy, defines structure      85
Horoball      39
Horocycles      40
Horospheres      38
Hyperbolic Dehn surgery theorem      104
Hyperbolic isometries      67
Hyperbolic line      10 13 14
Hyperbolic metric      11 13 17 39—40
Hyperbolic plane      10
Hyperbolic structure with nodes      346
Hyperbolic structures on a manifold      87
Hyperboloid      17
Hyperplane      13
Hyperplane and dual point      16 19
Ideal tetrahedra      45—48
Ideal tetrahedra, parametrization of      48
Ideal tetrahedra, volume of      160
Ideal triangles      40
Identifying faces of polyhedra      3
Incompressible surface      71
Incompressible surface and algebraic representations      143
Incompressible, suborbifold      324
Inner product      18 21
Intersection number      267 270
Irreducible, 3-manifold      2
Irreducible, orbifold      324
Jorgensen, T.      61 74 228
Jorgensen’s theorem      119—120
Jorgensen’s theorem, first version      116
Kleinian group      174
Kleinian group, manifold of      178
Kleinian structure      350
Knotted Y      31
Lamination      185 (see
Lamination on boundary of convex hull      186—187
Lamination, when isotopic to geodesic lamination      206
Law of cosines, hyperbolic      22
Law of sines, hyperbolic      25
Lickorish      2
Limit set      171
Limit set of a closed hyperbolic manifold      172
Link of a vertex      42
Link of an ideal tetrahedron      45—46
Links, $C_k$      144
Links, $D_{2k}$      150
Links, $F_n$      154
Links, having isomorphic complements      149
Lobachevsky      157
Manifold, affine      27—28
Manifold, differentiable      27
Manifold, elliptic      28—29
Manifold, hyperbolic      29
Margulis lemma      113
Measure topology on geodesic laminations      209
Measured lamination space      210 251
Metric of constant curvature and patterns of circles      338
Micky Mouse      194
Minimal set      172
Modular space      201
Mostow’s Theorem      101—102 106—112 129—130
Mumford      201
nodes      346
Orbifold      300
Orbifold with boundary      308
Orbifold, bad      304 324
Orbifold, classification of 2-dimensional      312
Orbifold, covering      303 305 311 313
Orbifold, Euler number      311
Orbifold, fundamental group      307
Orbifold, good      304 310 312
Orbifold, hyperbolic structure      314—318
Pair of pants      90
Papakyriakopoulos      2
parallel      14
Pared manifolds      259
Pleated surface      see “Uncrumpled surface”
Poincare dodecahedral space      320
Prasad      102
Projective lamination space      209 210 263
Properly discontinuous action      174
Pseudo-isometry      106
Pseudogroup      27
Pythagorean theorem, hyperbolic      25
Quasi-conformal map      110
Quasi-Fuchsian group      192 215
Quasi-Fuchsian group, mapping surfaces into      194
Quasi-isometric vector field      290
Quasi-isometry      285
Rational depth      252
Reflection group      323
Riley, R.      29 74 168
Schottky group      173
Seifert fibration      64
Singular locus      302 308
Smear      127
Sphere at infinity      11
Suborbifold      308
Sufficiently large      71
Sullivan      277
Symmetry of 2-generator 3-manifold      94
Tangent space of an orbifold      318
Teichmuller space      88 89—92
Teichmuller space for hyperbolic orbifold      318
Teichmuller space of the boundary of a 3-manifold      97
Thick-thin decomposition      112
Thick-thin decomposition for an orbifold      346
Thick-thin decomposition, characterization of $M_{(0,\epsilon]}      115
Three-punctured sphere      36
Tractrix      10
Train track      205
Train track, dual      267 271
Transverse measure      189
Ultraparallel      14
Uncrumpled surface [pleated]      200 219 249
Uncrumpled surface [pleated], realizing essentially complete lamination      249—251
Unit tangent bundle of orbifold      319—323
Visual average      285
Volume and Gromov’s invariant      126—128
Volume is a continuous function      119
Volume is well-ordered      139
Volume of a straight k-simplex      124
Volume, goes down after Dehn filling      138
Waldhausen      142
Whitehead link      32—33 120
Whitehead link, commensurable with Borromean rings      141
Whitehead link, volume of complement      165
Wrinkling locus      201 209
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