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Adams C.C. — The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
Adams C.C. — The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots

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Название: The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots

Автор: Adams C.C.

Аннотация:

You can do a lot with a knot. You can tie your shoe, tie your tie, or even tie your little brother to a chair, and on the way learn a great deal about topology, geometry, and even algebra. Adams gives basic information about the art and science of knot tying, and then expands this to describe tabulating knots; invariants of knots; surfaces and knots; types of knots; polynomials; knots in biology, chemistry and physics; knots, links and graphs; topology; and higher dimensional knotting. He includes many knotty problems and their solutions and even some knotty jokes.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 306

Добавлена в каталог: 14.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A-split      156
Achiral      15
Alexander polynomial      32 148 165 229
Alexander polynomial, of a splittable link      167
Alexander, J.      148
Algebraic link      48
Algebraic tangle      48
Almost alternating link      139
Almost alternating projection      139
Alternating knots and links      7 68 69 100 105 156
Alternative links      105
Ambient isotopy      12
Amphicheiral knot      15 176
Amphicheirality and alternating knots      178
And torus knots      142
Annulus      93
Appel, Kenneth      4 234 258
Arborescent link      48
Arf invariant      213 223 228
Aumann, Robert      143
B-split      156
Bleiler, Steve      61
Boltzmann constant      207
Bonahon, Francis      106
Borromean rings      17 22
Boundary components      87
Bracket polynomial      149
Bracket polynomial, and Reidemeister moves      149
Braid      127
Braid index      132 175
Braid index and crossing number      132
Braid index and Seifert circles      132
Braids, multiplication of      134
Bridge number      64
Brunnian link      22
Cable knot      118
Calugareanu, Georges      187
Capping off a surface with boundary      88
Catenane      198
Caudron, Alain      33
Chemically achiral      202
Chemically chiral      202
Closed braid representation      128
Closure of the braid      128
Codimension two      265
Color dimension      270
Compact      83 249
Companion knot      115
Complement of a knot      84 243 249
Complete graph      215
components      17
Composite knot      8 93
Composition of knots      7
Composition of knots, and genus      100
Compressible surface      86
Compression      86
Conjugation      137
Connected sum      81
Continued fractions      44
Conway sphere      94
Conway's notation      46
Conway, John R      33 41 141 166 217
Core curve      112
Cozzarelli, Nicholas      189
Crossing number      30 67
Crossings      3
Cube-with-holes      78
Culler, Marc      60
Cyclic DNA      183
Cyclic duplex DNA      184
Dehn surgery      259
Dehn, Max      177
Depth of a link      169
Dichromatic polynomial      231
Dietrich — Buchecker, Christina      199
Direct repeats      191
DNA      181
Double helix      182
Double of a manifold      242
Dowker notation      35
Dowker, Hugh      33
Embedding      78
Embedding, of a graph      216
Energy of interaction      207
Ernst, Claus      34 66 193
Euclidean metric      120
Euler characteristic      79
Euler characteristic, invariance of      79—81
Euler characteristic, of connected sum      82
Expansion of a graph      221
Factor knots      8
Figure-eight knot      3 25 176
Five-space      273
Flat metric      120
Flype      164
Four-color theorem      4 234
Franks, John      175
Fuller, Brock      187
Gabai, David      106 261
Gauss, Carl Friedrich      31
General position      102
Genus      78 93
Genus, of a knot      99
Geodesic      121
Gordon, Cameron      60 217 261
Graph      51 215
Group      135
Haken, Wolfgang      4 113 234 258
Hamiltonian cycle      222
Haseman, Mary G.      32
Hass, Joel      277
Hayashi, Chuichiro      146
Heegard splitting      255
Homeomorphic      76
Homeomorphism type      78
Homfly polynomial      148 165 169
Hopflink      18
Hopflink, bracket polynomial of      151
Human knot number      278
Hyperbolic geometry      121
Hyperbolic knot      119 120 123 127
Hyperbolic metric      121
Hyperbolic three-space      121
Hyperbolic volume      123
Incompressible      86
Int enzyme      193
Intrinsically knotted      231
Intrinsically linked      220
Invariant      21 174 160
Inverted repeats      191
Invertible      11
Ising model      205 213
Ising, E.      205
Isomorphic graphs      215
Isotopic surfaces      73
Isotopy      12 73
Jones polynomial      148 213
Jones polynomial, and X polynomial      154
Jones polynomial, of a torus knot      155
Jones, Vaughan      148 155 169 205
k-equivalent      63
k-move      62
Kanenobu, Taizo      60
Kauffman, Louis      68 148 223
Kinoshita — Terasaka mutants      49 106 174
Kirby calculus      263
Kirby, Robion      263
Kirkman, Thomas R      31
Klein bottle      91
Knot      2
Knot exterior      258
Knot in ${S}^{2}\times{S}^{1}$      253
Kronecker delta function      212 239
Kronheimer, Peter      113
Lattice      205
Laurent polynomial      147
Lens space      254
Lickorish, Raymond      260
Link      17
Linking number      18 187
Little, C N.      5 32
longitude      108
Lord Kelvin (William Thomson)      5 31
Luecke, John      60 261
m-almost alternating knot      144
Markov equivalent      137
Markov's theorem      137
Markov, A. A.      137
Maximal overpass      64
Menasco, William      163 165
Meridian      108
Meridional disk      112
Mobius band      90 94 184 278
Morton, Hugh      105 175
Mrowka, Tom      113
Murakami, Hitoshi      60
Murasugi, Kunio      68 111
Mutants      49 174
Mutation      49
n-embeddable knot      114
Nakanishi, Y      61 63
Negami, Seiya      30
Nonorientable      90
Ohyama, Yoshiyuki      132
One-skeleton      255
Orientable      90
Orientation      10
Overpass      64
Paquette, Leo      204
Partition function      208
Pass equivalent      223
Pass-move      223
Perko pair      32
Perko, Kenneth A.      32
Petersen graphs      221
Planar graphs      51
Planar isotopy      12
Poincare model      121
Poincare's conjecture      258
PoincarЈ, Henri      121 257
Potts model      213 239
Pretzel knot      48
Prime knot      9
Projection      3
Projections on the sphere      38
Property P      262
Rational link      46
Rational tangle      44
Reduced      68 159
Reduced alternating projection      159
Reidemeister move      13 55 149
Reidemeister, Kurt      14 31
Reshetikhin, Nikolai      263
Resolving tree      168
ribbon      184
Riley, Robert      119
Robertson, Neil      221
Satellite knot      115 126
Satellites, and composites      117
Sauvage, Jean-Pierre      199
Scharlemann, Martin      60 169 276
Seif ert, Herbert      95
Seifert circles      96 98 132
Seifert surfaces      95 99 224
Seifert surfaces, and incompressibility      100
Seifert surfaces, and orientability      97
Seymour, P. D.      221
Shalen, Peter      60
Shimabara, Miki      230
Siebenmann, Lawrence      106
Signed crossover number      185
Signed planar graph      52
Simmons, Howard III.      204
Simon, Jonathan      202
Simply connected      257
Site-specific recombination      190
Six-space      274
Skein relation      148 156
Smooth manifolds      272
Solid torus      112
span      160
Spin vector      206
Split union      171
Splittable link      17 84
Square bracket polynomial      235
Stabilization      137
Standardly embedded surface      114
Standardly embedded torus      113
Star-triangle relation      208
State      157
Stick number      29
Sticks      27
Substrate      191
Sumners, Dewitt      34 66 193
Supercoiling      188
surface      72
Surface, with boundary      87
Surfaces constructed from paper      89
Surgery      103
Swallow-follow torus      87
Synthesis of knotted molecules      195
Tait Flyping Conjecture      164
Tait, Peter Guthrie      5 32 164 178
Tangle      41
Tangles, equivalence of      41
Tetrahedralization      248
Thistlethwaite, Morwen      33 40 68 165 178
Thomas, Robin      221
Thompson, Abigail      169
Three-manifold      244
Three-sphere      246
Thurston, William      119 125
Tietze, H.      261
Time as the fourth dimension      267
Tn3 resolvase      193
Topoisomerase      182
Topological stereoisomer      197
Topologically achiral      201
Topologically chiral      201
topology      6
Toroidally alternating knot      145
Torus      71
Torus knots and unknotting number      113
Torus link      105 126
Torus with one boundary component      95
Trefoil knot      2 25 26 28 94 95 176 278
Triangulation      75
Triangulation, of a three-manifold      248
Tricolorability      23
Trivial knot      2
Trivial link      18
Trivial link, of two components      26
Tunnel number      114
Turaev, V. G.      263
Twist of a ribbon      185
Two-bridge knots      65
Two-embeddable knots      114
Two-manifold      73
Two-strand cable      116
Unknot      2 7 9 25
1 2
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