Topological library: 1 Cobordisms and their applications
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| Weitere Verfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai
World Scientific
2007
|
| Schriftenreihe: | Series on knots and everything
Vol. 39 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 369 Seiten |
| ISBN: | 9789812705594 |
Internformat
MARC
| LEADER | 00000nam a2200000 cc4500 | ||
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| 001 | BV036045240 | ||
| 003 | DE-604 | ||
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| 007 | t | ||
| 008 | 100222s2007 |||| 00||| eng d | ||
| 020 | |a 9789812705594 |c hardcover |9 978-981-270-559-4 | ||
| 035 | |a (OCoLC)633733852 | ||
| 035 | |a (DE-599)BVBBV036045240 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-83 |a DE-11 | ||
| 084 | |a SK 280 |0 (DE-625)143228: |2 rvk | ||
| 245 | 1 | 0 | |a Topological library |n 1 |p Cobordisms and their applications |c eds. S. P. Novikov (Landau Institute for Theoretical Physics, Russia & University of Maryland, USA), I. A. Taimanov (Sobolev Institute of Mathematics, Russia). Translated by V. O. Manturov |
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai |b World Scientific |c 2007 | |
| 300 | |a XIV, 369 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on knots and everything |v Vol. 39 | |
| 490 | 0 | |a Series on knots and everything | |
| 650 | 0 | 7 | |a Kobordismus |0 (DE-588)4148171-9 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4143413-4 |a Aufsatzsammlung |2 gnd-content | |
| 689 | 0 | 0 | |a Kobordismus |0 (DE-588)4148171-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Novikov, Sergej P. |d 1938-2024 |0 (DE-588)118786490 |4 edt | |
| 700 | 1 | |a Tajmanov, Iskander Asanovič |d 1961- |0 (DE-588)1051919274 |4 edt | |
| 700 | 1 | |a Manturov, V. O. |0 (DE-588)1023474107 |4 trl | |
| 773 | 0 | 8 | |w (DE-604)BV035821830 |g 1 |
| 830 | 0 | |a Series on knots and everything |v Vol. 39 |w (DE-604)BV004608347 |9 39 | |
| 856 | 4 | 2 | |m Digitalisierung UB Augsburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018937025&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
Datensatz im Suchindex
| _version_ | 1805076308698333184 |
|---|---|
| adam_text |
Contents
S. P. Novikov's
Preface
1
L. S. Pontrjagin.
Smooth manifolds and their
applications in homotopy theory
(Translated by V.
0.
Manturov)
1
Introduction
. 1
Chapter I. Smooth manifolds and their maps
. 3
§ 1.
Smooth manifolds
. 3
§2.
Embedding of a manifold into Euclidean space
. 12
§ 3. Nonproper
points of smooth maps
. 20
§ 4.
Non-degenerate singular points of smooth mappings
. 26
Chapter II. Framed manifolds
. 40
§ 1.
Smooth approximations of continuous mappings and
deformations
. 40
§ 2.
The basic method
. 45
§ 3.
Homology group of framed manifolds
. 57
§ 4.
The suspension operation
. 64
Chapter III. The
Hopf
invariant
. 68
§ 1.
Homotopy classification of mappings of
η
-manifolds to
the n-sphere
. 68
§ 2.
The
Hopf
invariant of mappings
ΣΆ+1
-*
Sk+1
. 74
§3.
Framed manifolds with
Hopf
invariant equal to zero
. 81
Chapter IV. Classification of mappings Sn+2
->
Sn
. 91
§1.
The Euclidean space rotation group
. 91
§ 2.
Classification of mappings
Σ3
—>
S2
. 99
§ 3.
Classification of mappings from (n
+
l)-sphere to n-sphere
105
§4.
Classification of mappings
Σ
("+2)-^
5". 115
References
. 129
viii
Contents
2
R.
Thom. Some "global" properties of
different iable manifolds
(
Translated by
V. 0.
Manturov with M. M. Postnikov 's
comments
(1958)) 131
Introduction
. 131
Chapter I, Properties of differentiable mappings
. 132
§ 1.
Definitions
. 132
§2.
Pre-image of a regular value
. 132
§ 3.
Properties of the critical values set
ƒ
(Σ)
. 134
§
3a. Pre-image of a manifold
. 135
§ 4.
Pre-image of a manifold under a ¿-regular mapping
. . 137
§ 5.
The
isotopy
theorem
. 140
Chapter II. Submanifolds and homology classes of
a manifold
. 141
§1.
Formulation of the problem
. 141
§ 2.
The space adjoint to a subgroup of the orthogonal
group
. 142
§ 3.
The main theorem
. 143
§4.
The case when
G
reduces to the unit element
e
Є
O(k)
146
§5.
The structure of spaces M{O{k)) and
M
(SO
(к))
. 146
§6.
The homotopy type of M(O(k))
. 151
§7.
The space M(O(k)) for small
к
. 158
§8.
The complex M(SO(
к)).
Stationary case
. 162
§ 9.
The space
M
(SO
(к))
for small
к
. 166
§ 10.
The multiplication theorem
. 168
§11.
Summary of results
. 172
Chapter III. On Steenrod's problem
. 174
§1.
Statement of the problem
. 174
§ 2.
Definition. Manifolds associated with a given finite
polyhedron
К
. 174
§3.
Applications. The case of modulo
2
coefficients
. 176
§4.
Operations tff
. 177
§5.
Steenrod's powers in cohomology algebras of
differentiable manifolds
. 180
Chapter IV. Cobordant differentiable manifolds
. 181
§1.
Invariants of cobordism classes
. 183
§ 2.
Differentiable mappings of manifolds with boundary
. 183
§3.
¿-equivalent manifold
. 186
Contents
ix
§4.
The basic theorem
. 192
§5.
Modulo
2
class groups 0Tfc
. 193
§ 6.
Multiplicative structure of the groups *Xtfe
. 195
§ 7.
The groups
Пк
. 199
Editor's remarks
. 203
References
. 207
3
S. P. Novikov. Homotopy properties of
Thom complexes (Translated by V.
0.
Manturov)
211
Introduction
. 211
Chapter I. Thorn's spaces
. 213
§ 1.
G-framed submanifolds. L-equivalence submanifold classes
. 213
§2.
Thom spaces. Classifying properties of Thom spaces
. 215
§ 3.
Cohomology of Thom spaces modulo p, where
p
> 2 . 217
§ 4.
Cohomology of Thom spaces modulo
2. 220
§ 5.
Diagonal homomorphisms
. 224
Chapter II. Inner homology rings
. 226
§1.
Modules with one generator
. 227
§ 2.
Modules over the Steenrod algebra
. 230
§3.
Modules over the Steenrod algebra. The case
p
= 2. 232
§ 4.
Inner homology rings
. 235
§ 5.
Characteristic numbers and the image of the Hurewicz
homomorphism in Thom spaces
. 237
Chapter III. Realization of cycles
. 242
§1.
Possibility of G-realization of cycles
. 242
References
.·. 249
4
S.
Smale.
Generalized
Poincaré's
conjecture
in dimensions greater than four
251
5
S.
Smale.
On the structure of manifolds
269
6
D. Quillen. On the formal group laws of
unoriented and complex cobordism theory
285
Contents
V.
M. Buchstaber, A. S. Mishchenko,
S. P. Novikov.
Formal groups and their role
in algebraic topology approach
(Translated by V.
0.
Manturov)
293
Introduction
. 293
§ 1.
Formal groups
. 293
§ 2.
Cobordism and bordism theories
. 296
§ 3.
The formal group of geometrical cobordisms
. 301
§ 4.
Two-valued formal groups and power systems
. 305
§ 5.
Fixed points of periodic transformations in terms of formal
groups
. 308
Appendix I
. 313
Appendix II
. 318
References
. 319
8
V. M. Buchstaber, S. P. Novikov. Formal groups,
power systems and Adams operators
(Translated by M. L. Glasser)
323
§1.
Formal groups
. 324
§ 2.
Formal power systems and Adams operators
. 332
§2a
. 337
§2b
. 345
§3.
Fixed points of transformations of order
ρ
. 351
Appendix
. 359
References
. 364
Index
367 |
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| spelling | Topological library 1 Cobordisms and their applications eds. S. P. Novikov (Landau Institute for Theoretical Physics, Russia & University of Maryland, USA), I. A. Taimanov (Sobolev Institute of Mathematics, Russia). Translated by V. O. Manturov New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai World Scientific 2007 XIV, 369 Seiten txt rdacontent n rdamedia nc rdacarrier Series on knots and everything Vol. 39 Series on knots and everything Kobordismus (DE-588)4148171-9 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Kobordismus (DE-588)4148171-9 s DE-604 Novikov, Sergej P. 1938-2024 (DE-588)118786490 edt Tajmanov, Iskander Asanovič 1961- (DE-588)1051919274 edt Manturov, V. O. (DE-588)1023474107 trl (DE-604)BV035821830 1 Series on knots and everything Vol. 39 (DE-604)BV004608347 39 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018937025&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Topological library Series on knots and everything Kobordismus (DE-588)4148171-9 gnd |
| subject_GND | (DE-588)4148171-9 (DE-588)4143413-4 |
| title | Topological library |
| title_auth | Topological library |
| title_exact_search | Topological library |
| title_full | Topological library 1 Cobordisms and their applications eds. S. P. Novikov (Landau Institute for Theoretical Physics, Russia & University of Maryland, USA), I. A. Taimanov (Sobolev Institute of Mathematics, Russia). Translated by V. O. Manturov |
| title_fullStr | Topological library 1 Cobordisms and their applications eds. S. P. Novikov (Landau Institute for Theoretical Physics, Russia & University of Maryland, USA), I. A. Taimanov (Sobolev Institute of Mathematics, Russia). Translated by V. O. Manturov |
| title_full_unstemmed | Topological library 1 Cobordisms and their applications eds. S. P. Novikov (Landau Institute for Theoretical Physics, Russia & University of Maryland, USA), I. A. Taimanov (Sobolev Institute of Mathematics, Russia). Translated by V. O. Manturov |
| title_short | Topological library |
| title_sort | topological library cobordisms and their applications |
| topic | Kobordismus (DE-588)4148171-9 gnd |
| topic_facet | Kobordismus Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018937025&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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