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Lando S.K., Zvonkin A.K. — Graphs on Surfaces and Their Applications
Lando S.K., Zvonkin A.K. — Graphs on Surfaces and Their Applications



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Название: Graphs on Surfaces and Their Applications

Авторы: Lando S.K., Zvonkin A.K.

Аннотация:

Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.


Язык: en

Рубрика: Математика/Алгебра/Комбинаторика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 459

Добавлена в каталог: 30.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Polynomial, Conway      356
Polynomial, decomposable      311
Polynomial, defining      89 114
Polynomial, Gegenbauer      130
Polynomial, Hermite      187
Polynomial, HOMFLY      357
Polynomial, Jacobi      130
Polynomial, Legendre      130
Polynomial, matching      365
Polynomial, Shabat      80
Polynomial, square-free form of      84
Polynomial, trigonometric      268
Positive resolution of a singular point      342
Positive triangle      50
Preinvariant      353
Primitive group      7
Primitive stratum      272
Primitive, element of a bialgebra      337
Principal part      285
Product, semidirect      65
Product, wreath      66
Projection      13
Protective line, complex      69
Protective linear group      47
Protective special group      48
Psendorhombicuboctahedron      111
Pure Belyi function      108
Pure braid group      297
Purely cubic field      103
Qnasihomogeneoiis mapping      266
Quadrangle edge      364
Quadrangle vertex      363
Quadratic Jenkins — Strebel differential      232
Quadratic Jenkins — Strebel differential, canonical      233
Quadratic residue      220
Quasi-elliptic integral      140
Quasimodnlar form      415
Quotient constellation      67
Ramification locus      20 71
Ramification point      14 20
Ramified covering      14
Reciprocal hypermap      52
Refined passport      8
Regular constellation      68
Regular, covering      17
Renormalization operator      352
Representation of a group      389
Representation of a group, irreducible      390
Representation of a group, irreducible, character of      390
Representation of a group, left      389
Representation of a group, right      389
Representations, isomorphic      389
Residue of a meromorphic 1-form      217
Residue, quadratic      220
Resolution of a singular point, negative      342
Resolution of a singular point, positive      342
Ribbon graph      1
Riemann data      73
Riemann sphere      69
Riemann surface      69
Riemann surfaces, isomorphic      69
Riemann — Hurwitz formula      21
Riemann’s existence theorem      73
Rigid, classification of coverings      23 262 269
Rigid, equivalence of coverings      23
Rigidity      75
Ritt theorem      64 309
Root      44
Rooted cactus      57
Rooted hypermap      44
Sato, Grassmanian      201
Sato, subspace      201
Schur's lemma      390
Second Orthogonality Relation      393
Segre class      284
Segre class, top      284
Self-dual map      53
Semidirect product      65
Semilinear transformation      48
Set, Fatou      137
Set, Julia      137
Set, Mandelbrot      137
Shabat polynomial      80
Shabat polynomials, equivalent      82
Sheet      13
Sheets of a curve at a double point      217
Simple critical value      301
Simple graph      360
Singular knot      342
Solid, Archimedean      111
Solid, platonic      111
Solution, parasitic      90
Space, Hurwitz      279 320
Space, Hurwitz, completed      289
Space, moduli, coarse      226
Space, moduli, fine      226
Spanning subgraph      372
Special cactus      309
Special group      7
Special linear group      48
Special map      39
Special tree      47
Sphere braid group      297
Splitting field      114
Sporadic tree      98
Square free form of a polynomial      84
Stabilizer of a point      221
Stable curve      227
Stable meromorphic function      290
Stable pair (g, n)      225
Standard Gaussian measure      159
Star graph      17 22
Stationary equation      196
Stratum      270
Stratum, Maxwell      271
Stratum, primitive      272
Strictly preperiodic point      137
String equation      246
STU-relation      384
surface      21
Surface, braid group      297
Symmetric cactus      57
Symmetric matrix      163
Symmetry, order of      57
Temperley — Lieb algebra      386
Theorem, Belyi      77
Theorem, Feit — Jones      318
Theorem, Kontsevich      249
Theorem, Mueller      309
Theorem, Riemann's existence      73
Theorem, Ritt      64; 309
Top Segre class      284
Topological map      27
Transformation, elementary      343
Transformation, semilinear      48
TREE      43
Tree, bicolored plane      43
Tree, canonically labelled      44
Tree, diameter of      98
Tree, plane      43
Tree, plane, canonical geometric form of      85
Tree, special      47
Tree, sporadic      98
Tree, valuable passport      44
Trees, conjugate      89
Trees, family of      92
Triangle, negative      50
Triangle, positive      50
Triangulation, canonical      50
Triangulation, elementary      51
Trigonometric polynomial      268
Tutte, invariant      359
Tutte, relation      359
Type of a composition      312
Unicursal curve      183
Unitary group      167
Unitary matrix      167
Universal covering      17
Universal curve      227
Universal enveloping algebra      377
Universal Galois group      113
Universal one-matrix model      199
Unramified covering      12
Valency      26
Valency of      26
Valency of a face      29
Valency of a vertex      26
Valuable cactus passport      58
Valuable tree passport      44
Value, critical      14 20 79
Vassiliev invariant      344
Vertex      26
Vertex, degree of      26
Vertex, external      384
Vertex, internal      384
Vertex, quadrangle in a graph      363
Virtual Euler characteristic      223
Weight of a C*-action      266
Weight of a coordinate      266
Weight of a weighted graph      370
Weight system      353
Weight system, complete      381
Weight system, multiplicative      353
Weighted 3-term element      370
Weighted graph      370
Weighted graph invariant      371
Weighted graph invariant, multiplicative      371
Weighted graphs, bialgebra of      370
Whitehead collapse      230
Whitney formula      285
Wick coupling      160
Witten conjecture      249
Wreath product      66
Zannier bound      127
Zero of a meromorphic function      7
1 2 3
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