Topology and geometry for physicists:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Mineola, New York
Dover Publications, Inc.
2011
|
| Edition: | This Dover edition, first published in 2011, is an unabridged republication of the work originally published in 1983 by Academic Press, Inc., New York |
| Series: | Dover books on mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index. - Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | VIII, 311 Seiten Illustrationen 22 cm |
| ISBN: | 9780486478524 0486478521 |
Staff View
MARC
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| 100 | 1 | |a Nash, Charles |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Topology and geometry for physicists |c Charles Nash, Department of Mathematical Physics, National University of Ireland, Maynooth, Ireland; Siddhartha Sen, School of Mathematics, Trinity College, Dublin, Ireland |
| 250 | |a This Dover edition, first published in 2011, is an unabridged republication of the work originally published in 1983 by Academic Press, Inc., New York | ||
| 264 | 1 | |a Mineola, New York |b Dover Publications, Inc. |c 2011 | |
| 300 | |a VIII, 311 Seiten |b Illustrationen |c 22 cm | ||
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| 490 | 0 | |a Dover books on mathematics | |
| 500 | |a Includes bibliographical references and index. - Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Topology | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Mathematical physics | |
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Record in the Search Index
| _version_ | 1804145636114694144 |
|---|---|
| adam_text | Contents
Preface iii
Chapter
1.
Basic Notions of Topology and the Value of Topological
Reasoning
1.1.
Introduction
..................... 1
1.2.
Basic topological notions
............... 8
1.3.
Homeomorphisms, homotopy and the idea of topological
invariants
..................... . 20
1.4.
Topological invariants of compactness and connectedness
. 22
1.5.
Invariance
of the dimension of R
........... . 23
Chapter
2.
Differential Geometry: Manifolds and Differential Forms
2.1.
Manifolds
...................... 25
2.2.
Orientability
..................... 33
2.3.
Calculus on manifolds
................. 37
2.4.
Infinite dimensional manifolds
............. 49
2.5.
Differentiable structures
................ 49
Chapter
3.
The Fundamental Group
3.1.
Introduction
..................... 51
3.2.
Definition of the fundamental group
.......... 56
3.3. Simplexes
and the calculating theorem
.......... 67
3.4. Triangulation
of a space with examples
......... 70
3.5.
Fundamental group of a product
X x Y .........
77
Chapter
4.
The Homology Groups
4.1.
Introduction
..................... 79
4.2.
Orientedsimplexesandthedefinitionofthehomologygroups
. 83
4.3.
Abelian groups
.................... 90
4.4.
Relative homology groups
............... 95
4.5.
Exact sequences
................... 99
v
VÍ
CONTENTS
4.6. Torston, Kunneth
formula, Euler-Poincaré formula
and sin¬
gular homology
................... 104
Chapter
5.
The Higher Homotopy Groups
5.1.
Introduction
..................... 109
5.2.
Definition of higher homotopy groups
.......... 109
5.3.
Abelian nature of higher homotopy groups
........ 112
5.4.
Relative homotopy groups
............... 113
5.5.
The exact homotopy sequence
............. 116
Chapter
6.
Cohomology and
De Rham
Cohomology
6.1.
Introduction
..................... 120
6.2.
НР(М;Я)
and
Poincaré s
lemma
............ 123
6.3.
Poincaré s
lemma
................... 125
6.4.
Calculation of HP(M;R)
............... 127
6.5.
General remarks
................... 136
6.6.
The cup product
................... 137
6.7.
Superiority of cohomology over homology
........ 138
Chapter
7.
Fibre Bundles and Further Differential Geometry
7.1.
Introduction
.................... 140
7.2.
Fibre bundle
.................... 141
7.3.
More examples of bundles
.............. 148
7.4.
When is a bundle trivial?
............... 152
7.5.
Sections of bundles and singularities of vector fields
. . . 156
7.6.
Cutting a bundle down to size: reduction of the group and
contraction of the base space
............. 159
7.7.
Remarks on almost Hamiltonian and almost complex
structures
...................... 165
7.8.
G-structures on a compact closed manifold
M
...... 171
7.9.
Lie derivative
.................... 171
7.10.
Connection and curvature
.............. 174
7.11.
The connection form and the gauge potential
...... 177
7.12.
Parallel transport, covariant derivative and curvature
. . . 178
7.13.
Covariant exterior derivatives
............. 181
7.14.
The
Bianchi
identities and *F
............. 182
7.15.
Connection in the tangent bundle
........... 184
7.16.
The torsion tensor
.................. 187
7.17.
Geodesies
..................... 190
CONTENTS
VU
7.18.
The Levi-Civita
connection
.............. 191
7.19.
The Yang-Mills connection
.............. 194
7.20.
The Maxwell connection
............... 196
7.21.
General remarks
.................. 198
7.22.
Characteristic classes
................. 200
7.23.
Chern, Pontrjagin and
Euler
classes
.......... 204
7.24.
Characteristic classes in terms of curvature and invariant
polynomials
..................... 206
7.25.
Classification of bundles
............... 211
7.26.
The
Stiefel-Whitney
class
............... 212
7.27.
Calculation of characteristic classes
........... 213
7.28.
General remarks
.................. 217
7.29.
Formulae obeyed by characteristic classes
........ 219
7.30.
Global invariants and local geometry
.......... 221
Chapter
8.
Morse Theory
8.1.
More inequalities
................... 227
8.2.
Morse lemma
.................... 229
8.3.
Symmetry breaking selection rules in crystals
....... 236
8.4.
Estimating equilibrium positions
............ 242
Chapter
9.
Defects, Textures and Homofopy Theory
9.1.
Planar spin in two dimensions
............. 244
9.2.
Definition of an ordered medium
............ 245
9.3.
Stability of
def
ects theorem
.............. 246
9.4.
Examples
...................... 250
9.5.
General remarks and crossing of defects, textures and
1гз(Ѕ2)
251
Chapter
10.
Yang-Mills Theories:
Instantons
and
Monopoles
10.1.
Introduction
.................... 256
10.2.
Instantons
..................... 259
10.3.
Topology and boundary conditions
.......... 260
10.4.
Instantons
and absolute minima
........... 263
10.5.
The
instanton
solution
.............. . 265
10.6.
The
instanton
number and the second Chern class
. . . 269
10.7.
Multi-instantons
.................. 272
10.8.
Quaternions and SU(2) connections
......... 272
10.9.
The
k
= 1
instanton
in terms of quaternions
...... 276
10.10.
Instantons
with k >1 and quaternions
........ 278
Viii CONTENTS
10.11.
Example
of
instantons
with
|fe|>l
.......... 281
10.12.
Twistor methods and
instantons
........... 283
10.13.
The projective twistor space
............. 283
10.14.
Twistor space and planes in C4
............ 285
10.15.
a-planes and anti-self-dual connections
........ 288
10.16.
The equivalence between
instantons
and holomorphic vec¬
tor bundles
.................... 289
10.17.
Construction of an
instanton
given a holomorphic vector
bundle
...................... 295
10.18.
The Minkowski case
................ 297
10.19.
Monopoles
.................... 297
10.20.
The
Bohm-
Aharanov effect
............. 301
Further Reading
..................... 305
Subject Index
...................... 306
|
| any_adam_object | 1 |
| author | Nash, Charles Sen, Siddhartha |
| author_GND | (DE-588)13199218X |
| author_facet | Nash, Charles Sen, Siddhartha |
| author_role | aut aut |
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| bvnumber | BV037347768 |
| classification_rvk | SK 280 SK 950 |
| ctrlnum | (OCoLC)630478081 (DE-599)BVBBV037347768 |
| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | This Dover edition, first published in 2011, is an unabridged republication of the work originally published in 1983 by Academic Press, Inc., New York |
| format | Book |
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| id | DE-604.BV037347768 |
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| indexdate | 2024-07-09T23:22:36Z |
| institution | BVB |
| isbn | 9780486478524 0486478521 |
| language | English |
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| physical | VIII, 311 Seiten Illustrationen 22 cm |
| publishDate | 2011 |
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| publisher | Dover Publications, Inc. |
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| series2 | Dover books on mathematics |
| spelling | Nash, Charles Verfasser aut Topology and geometry for physicists Charles Nash, Department of Mathematical Physics, National University of Ireland, Maynooth, Ireland; Siddhartha Sen, School of Mathematics, Trinity College, Dublin, Ireland This Dover edition, first published in 2011, is an unabridged republication of the work originally published in 1983 by Academic Press, Inc., New York Mineola, New York Dover Publications, Inc. 2011 VIII, 311 Seiten Illustrationen 22 cm txt rdacontent n rdamedia nc rdacarrier Dover books on mathematics Includes bibliographical references and index. - Hier auch später erschienene, unveränderte Nachdrucke Topology Geometry, Differential Mathematical physics MATHEMATICS / Topology bisacsh Mathematische Physik Topologie (DE-588)4060425-1 gnd rswk-swf Physiker (DE-588)4045968-8 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s DE-604 Topologie (DE-588)4060425-1 s Physiker (DE-588)4045968-8 s 1\p DE-604 Sen, Siddhartha Verfasser (DE-588)13199218X aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022501319&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nash, Charles Sen, Siddhartha Topology and geometry for physicists Topology Geometry, Differential Mathematical physics MATHEMATICS / Topology bisacsh Mathematische Physik Topologie (DE-588)4060425-1 gnd Physiker (DE-588)4045968-8 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4045968-8 (DE-588)4012248-7 |
| title | Topology and geometry for physicists |
| title_auth | Topology and geometry for physicists |
| title_exact_search | Topology and geometry for physicists |
| title_full | Topology and geometry for physicists Charles Nash, Department of Mathematical Physics, National University of Ireland, Maynooth, Ireland; Siddhartha Sen, School of Mathematics, Trinity College, Dublin, Ireland |
| title_fullStr | Topology and geometry for physicists Charles Nash, Department of Mathematical Physics, National University of Ireland, Maynooth, Ireland; Siddhartha Sen, School of Mathematics, Trinity College, Dublin, Ireland |
| title_full_unstemmed | Topology and geometry for physicists Charles Nash, Department of Mathematical Physics, National University of Ireland, Maynooth, Ireland; Siddhartha Sen, School of Mathematics, Trinity College, Dublin, Ireland |
| title_short | Topology and geometry for physicists |
| title_sort | topology and geometry for physicists |
| topic | Topology Geometry, Differential Mathematical physics MATHEMATICS / Topology bisacsh Mathematische Physik Topologie (DE-588)4060425-1 gnd Physiker (DE-588)4045968-8 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Topology Geometry, Differential Mathematical physics MATHEMATICS / Topology Mathematische Physik Topologie Physiker Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022501319&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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