Virtual knots: the state of the art
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2013
|
| Schriftenreihe: | Series on knots and everything
51 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXV, 521 S. Ill., graph. Darst. |
| ISBN: | 9814401129 9789814401128 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV040593201 | ||
| 003 | DE-604 | ||
| 005 | 20140403 | ||
| 007 | t | ||
| 008 | 121127s2013 ad|| |||| 00||| eng d | ||
| 010 | |a 2012010601 | ||
| 020 | |a 9814401129 |c hardcover : alk. paper |9 981-4401-12-9 | ||
| 020 | |a 9789814401128 |c hardcover : alk. paper |9 978-981-4401-12-8 | ||
| 035 | |a (OCoLC)820425969 | ||
| 035 | |a (DE-599)GBV715071343 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-824 |a DE-384 |a DE-703 |a DE-739 |a DE-29T | ||
| 050 | 0 | |a QA612.2 | |
| 084 | |a SK 300 |0 (DE-625)143230: |2 rvk | ||
| 100 | 1 | |a Manturov, V. O. |e Verfasser |0 (DE-588)1023474107 |4 aut | |
| 240 | 1 | 0 | |a Virtual'nye uzly |
| 245 | 1 | 0 | |a Virtual knots |b the state of the art |c Vassily Olegovich Manturov ; Denis Petrovich Ilyutko |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2013 | |
| 300 | |a XXV, 521 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on knots and everything |v 51 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 0 | 7 | |a Knoten |g Mathematik |0 (DE-588)4164314-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Knoten |g Mathematik |0 (DE-588)4164314-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Ilyutko, Denis Petrovich |e Verfasser |0 (DE-588)1023473550 |4 aut | |
| 830 | 0 | |a Series on knots and everything |v 51 |w (DE-604)BV004608347 |9 51 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025421091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025421091 | ||
Datensatz im Suchindex
| _version_ | 1804149679692185600 |
|---|---|
| adam_text | Index
IT-Relation, 288
iT-Relation,
310
generalized,
310
4-
Graph,
354
minimal,
392
simplifiable,
392
éT-Relation,
288
generalized,
291
Л
-State,
128, 490
A-Structure,
129
S-State,
128, 490
B-Structure,
130
./-Invariant,
292
VA-Polynomial,
82
¿¿-Diagram,
136
framed,
136
/-Graph,
137
A;-Graph,
2
fc-Tr an
sfor
mation,
313
n-System,
275
ordered,
275
virtual,
271
Admissible word set,
62
Alexander module,
79
Annulus
essential,
52
inessential,
52
vertical,
31
Arc,
4, 60, 61, 113
long,
60
non-compact,
94
of a chord diagram,
133
short,
61
trivial,
34
vertical,
34
Arrow
bad,
297
Atom,
128
connected,
128
height,
130
orientable,
128
spherical,
129
torus,
129
Axiomatice
of parity,
353
Borromean rings,
4
Boundary,
182
Braid
pure,
22
virtual,
258, 259
even,
259
pure,
259
Branch,
3
Breaking,
96
Burau
representation,
266
Cable,
145, 147
Categorification,
177
Chain,
182
Changing circuit,
329
Chord,
133
even,
351
515
516
Virtual Knots: The State of the Art
Gaussian,
316
non-
Gaussian
with framing
0, 316
with framing
1, 316
odd,
351
Chords
linked,
134
unlinked,
135
Circle
core,
133
horizontal,
34
innermost,
34
outermost,
34
subcriticai,
129
supercritical,
129
trivial,
34
Circuit
Gauss,
312, 316
rotating,
312, 316
Closure,
95, 377
Kishino,
307
of a virtual braid,
261
Cobordism
atomic,
449
checkerboard,
449
combinatorial,
420
elementary,
421
of words,
422
two-atomic,
449
Coboundary,
182
Cochain,
182
Co cycle,
182
Collection
admissible,
151
Coloring
monochrome,
57
proper,
57, 78
Complex
Khovanov,
177
topological,
179
Koszul,
178
Wehr
li,
245
Complexes
quasiisotopic,
183
Component
of a hierarchy link,
113
of a link,
1
unicursal,
9
Configuration
even symmetric,
421
Covering
orientable,
130, 206
Crossing,
3
even,
363
flat,
16
flat classical,
16
negative,
3
odd,
26, 363
of first type,
427
of second type,
427
positive,
3
semivirtual,
293
splitting,
244
virtual,
8
Cube
anticommutative,
186, 197
bifurcation,
184, 186
commutative,
197
state,
139
Curve
left,
405
null-cobordant,
419
right,
405
singular,
292
slice,
419
Curves
homotopic,
403
Cusp,
435
Cycle,
182, 338
bad,
208
orientable,
209
right,
208
Degree,
2, 303
of an invariant,
294
Dehn
twist,
15
Derivative,
286
Destabilization,
22, 31
along annulus,
31
Diagonal,
255
Diagram
1-complete,
143
Index
517
2-complete,
256
M-hierarchy,
113
adequate,
146, 169
alternating,
3
chord,
132, 133, 287
connected,
348
dual,
173
framed,
133, 134, 315
labeled,
457
oriented,
134
connected,
4, 36, 145
descending,
296
Gauss,
10
irreducible,
352
odd,
352
hierarchy,
113
minimal.
143
non-orient able,
196
non-split,
492
of a knot,
3
of a virtual braid,
258
of a virtual link,
б
orientable,
196
proper,
60
quasialt
ernating,
145, 492
reduced,
142
regular,
270
semiadequate,
146
virtual,
8
connected,
9
long,
94
singular,
302
with semivirtual crossings,
293
Diagrams
cobordant,
421
Differential
partial,
185, 214
Dimension
graded,
182
Disc
boundary incompressible,
51
clean.
51
compressing,
50
inessential,
51
spanning,
420
Distance,
491
Double involution,
67
Edge,
2
bad,
208
cyclic,
2, 354
right,
208, 209
Edges
equivalent,
9
opposite,
2
Element
final,
98
initial,
98
Embedding
proper,
31
Equivalence
oriented,
138
Euler
characteristic
graded,
183
of an atom,
128
Euler
tour,
312, 313
Filtration, 380;
382
Vassiliev,
286
Form
normal,
25
Formula
combinatorial,
282
Frame of an atom,
128
Framing
of a chord,
457
of a vertex,
459
Frobenius extension,
245
Function
generalized weight,
292
generating,
346
Morse,
444
simple,
444
Genus
of a cobordism,
434
of a link,
36
of a virtual link,
131, 215
of an atom,
36, 128, 493
Seifert, 36, 38, 39
slice,
419, 433, 435
Turaev,
128, 215
518
Virtual
Knots: The State of the Art
underlying,
35
Grading,
182, 380
homoiogical,
182
quantum,
182
Graph
k-
valent,
2
adequate,
493
alternating,
492
framed,
2, 459
free framed,
462
realizable,
462
intersection,
308
labeled,
459
labeled,
459
looped,
463
looped interlacement,
453, 463
minimal,
488
non-realizable,
459
non-split,
493
realizable,
308, 459
Reeb,
444
simple,
2
underlying,
4
unicursal,
316
Graph-knot,
454, 465
Graph-link,
462
free,
455, 462
non-realizable,
455, 479
realizable,
465
Graph-move,
461
Group
classical,
75
of a braid,
22
of virtual braids,
259
stably,
261
virtual,
75
with peripheral structure,
58
Groupoid,
7, 58, 62
Height,
130, 131, 182, 191
of a Khovanov homology,
243
of a state,
184
of an edge,
197
Homotopy class
free,
455
non-realizable,
455, 479
of looped graphs,
454, 464
free,
464
realizable,
465
Hurwitz action,
275
Idempotency,
7, 62
Image
mirror,
313
Immersion
generic,
11, 419
Index,
382
of a chord,
382
of a crossing,
382
self-linking,
351
Whitney,
165
Invariant
coloring,
57
finite-type,
281, 286, 293
of order n,
292
quantum,
xviii, 25, 281
universal Vassiliev—Kontsevich,
281
Vassiliev,
281, 286
Isomorphism
of framed 4-graphs,
2
of virtual quandles,
71
Isotopy,
1, 4
rigid,
283
Kauffman bracket,
123, 491
even,
411
for rigid knots,
166
Khovanov homology,
182
Knot,
1, 359
classical,
1
figure eight,
4
free,
351, 355, 455
long,
356
Kishino,
357
long
classical,
94
trivial,
94
virtual,
94
null-cobordant,
435
oriented.
1
prime,
7
slice,
435
Index
519
trivial, 4
virtual,
8, 9
compact,
95
flat,
16, 357
rigid,
25, 164
singular,
303
twisted,
215
welded,
15
Knot complexity,
4
Knot group,
5, 57
Knots
combinatorially cobordant,
420
isotopie,
1
Label,
444
Level
sub critical,
129
supercritical,
129
Line
double,
432, 437
of first type,
441
of second type,
441
Link,
1
classical,
1
colored,
2
framed,
146, 289
free,
355, 455
hierarchy,
113
Hopf, 4
minimal representative,
31
orientable,
196
oriented,
1
framed,
2
singular,
285
trivial,
4
free,
355
virtual,
8, 9, 30
alternating,
205
oriented,
31
singular,
303
Whitehead,
4
Links
framed
isotopy.
2
Local complementation,
329, 460
Loop
free,
2
Manifold
boundary irreducible,
51
Haken, 52
irreducible,
50
sufficiently large,
51
Mapping
Frobenius,
245
functorial,
377
Markov transformation,
262
Matrix,
82
adjacency,
320, 465
Alexander,
79
generalized,
90
factorization,
178
Molecule,
444
Morphism
elementary,
359
Move
decreasing,
13
detour,
8
forbidden,
15
increasing,
13
local,
265
Markov,
24, 262
virtual,
24
Reidemeister,
4
first,
355
framed,
147
second,
355
third,
355
virtual,
12
semivirtual,
12
Mutant,
127
Mutation,
126
Number
crossing,
414
classical,
413
virtual,
413
of circles,
491
of components,
355, 465
self-linking,
26
writhe,
9, 465
Operation
decreasing,
322
520
Virtual Knots: The State of the Art
pivot,
329
pivoting,
460
star,
314
framed,
317
Orientability
of an atom,
128
Orientation
alternating,
198
Overcrossing,
3, 258
early,
97, 98
Pairing
homological,
437
Parity,
360
Gaussian,
351, 362, 440
justified,
427, 441
of a double line,
441
justified,
427
relative,
381
universal,
368
weakened,
361
Pattern,
49
boundary,
51
Plate,
31
Point
crossing,
338
self-crossing,
338
self-tangency
direct,
290
inverse,
290
splitting,
140, 492
Polyák
algebra,
282
Polygon,
369
Polynomial
Alexander,
80
Jones,
214. 492
even,
411
Jones -Kauffman,
121, 123
Kauffman
surface,
162
Presentation
Dehn, 5
Wirtinger, 5, 57
Product
tensor
ordered,
219
unordered,
184
Projection,
381
Quandle,
7, 58, 62
long,
97
linear,
101
virtual,
59, 68
Relation
defining,
63
four-term,
288
one-term,
288
strange,
98
two-term,
310
generalized.
310
Vassiliev,
286
Representative
minimal,
50, 392
singular,
39
Result of surgery,
320
Section
regular,
428
singular,
427
Segment
odd of first type,
432
odd of second type,
432
Self-distributivity,
7, 62
Shadow,
4
Shift
grading,
182
height,
182
Sign
of a chord,
457
of a vertex,
459
Smoothing,
122, 362, 386
1-even,
386
even,
386
for a free framed graph,
480
Span of a polynomial,
142, 167
Stabilization,
22, 31
State,
386
neighboring,
490
of a diagram,
122
of a graph,
490
opposite,
490
Index
521
Strand of a braid,
23
Structure
of opposite edges,
2, 129
peripheral,
68
source—sink,
198
Subcube,
139
Subdiagram,
296, 377
Subgraph
even,
484
Sum
connected,
37, 38
classical,
39
of long virtual knots,
38
disconnected,
36
Summation
geometric,
30, 49
Surface
admissible,
33
basis,
49
boundary
compressible,
51
incompressible,
51
compressible,
51
essential,
33
fundamental,
49
incompressible,
51
normal,
29, 49
proper,
32, 49
spanning,
434
thickened,
31
Surgery,
309, 363
Symbol,
286
System
Frobenius,
245
weight,
289
Tangle
free,
388
Theory
closed,
377
of free knots,
16
of pseudoknots,
17
of quasiknots,
17
Thickening
orientable,
215
Thickness
of a complex,
255
of a diagram,
255
Torsion,
57
Trefoil,
4
Turaev delta,
406
Undercrossing,
3, 258
early,
97, 98
Universal
(Т^, Л)
-construction,
247
Unknot,
4
free,
355
Value
non-singular,
444
Vassiliev obstruction,
338
Vertex,
354
even,
362, 483, 487
with respect to a smoothing,
488
Gaussian,
315
non-
Gaussian
with framing
0, 316
with framing
1, 316
odd,
362, 483, 487
with respect to a smoothing,
488
oriented,
481
terminal,
386
Visualization,
16, 125
Width,
167
of a complex,
255
of a diagram,
255
Word
cyclic,
314
double occurrence,
314
framed.
315, 316
Gauss,
352
|
| any_adam_object | 1 |
| author | Manturov, V. O. Ilyutko, Denis Petrovich |
| author_GND | (DE-588)1023474107 (DE-588)1023473550 |
| author_facet | Manturov, V. O. Ilyutko, Denis Petrovich |
| author_role | aut aut |
| author_sort | Manturov, V. O. |
| author_variant | v o m vo vom d p i dp dpi |
| building | Verbundindex |
| bvnumber | BV040593201 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612.2 |
| callnumber-search | QA612.2 |
| callnumber-sort | QA 3612.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 300 |
| ctrlnum | (OCoLC)820425969 (DE-599)GBV715071343 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040593201 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:26:52Z |
| institution | BVB |
| isbn | 9814401129 9789814401128 |
| language | English |
| lccn | 2012010601 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025421091 |
| oclc_num | 820425969 |
| open_access_boolean | |
| owner | DE-824 DE-384 DE-703 DE-739 DE-29T |
| owner_facet | DE-824 DE-384 DE-703 DE-739 DE-29T |
| physical | XXV, 521 S. Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on knots and everything |
| series2 | Series on knots and everything |
| spelling | Manturov, V. O. Verfasser (DE-588)1023474107 aut Virtual'nye uzly Virtual knots the state of the art Vassily Olegovich Manturov ; Denis Petrovich Ilyutko New Jersey [u.a.] World Scientific 2013 XXV, 521 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on knots and everything 51 Includes bibliographical references and index Knoten Mathematik (DE-588)4164314-8 gnd rswk-swf Knoten Mathematik (DE-588)4164314-8 s DE-604 Ilyutko, Denis Petrovich Verfasser (DE-588)1023473550 aut Series on knots and everything 51 (DE-604)BV004608347 51 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025421091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Manturov, V. O. Ilyutko, Denis Petrovich Virtual knots the state of the art Series on knots and everything Knoten Mathematik (DE-588)4164314-8 gnd |
| subject_GND | (DE-588)4164314-8 |
| title | Virtual knots the state of the art |
| title_alt | Virtual'nye uzly |
| title_auth | Virtual knots the state of the art |
| title_exact_search | Virtual knots the state of the art |
| title_full | Virtual knots the state of the art Vassily Olegovich Manturov ; Denis Petrovich Ilyutko |
| title_fullStr | Virtual knots the state of the art Vassily Olegovich Manturov ; Denis Petrovich Ilyutko |
| title_full_unstemmed | Virtual knots the state of the art Vassily Olegovich Manturov ; Denis Petrovich Ilyutko |
| title_short | Virtual knots |
| title_sort | virtual knots the state of the art |
| title_sub | the state of the art |
| topic | Knoten Mathematik (DE-588)4164314-8 gnd |
| topic_facet | Knoten Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025421091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004608347 |
| work_keys_str_mv | AT manturovvo virtualnyeuzly AT ilyutkodenispetrovich virtualnyeuzly AT manturovvo virtualknotsthestateoftheart AT ilyutkodenispetrovich virtualknotsthestateoftheart |