Topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Chelsea Publ. Co.
1965
|
| Edition: | 2. ed., 2. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 413 S. |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | TABLE OF CONTENTS
Section Page
Preface iii
Preface v
Introduction 1
CHAPTER I
ELEMENTARY COMBINATORIAL THEORY OF COMPLEXES
1. The simplex, the cell, the sphere and the complex 7
2. Orientation. Chains. Cycles 14
3. Arithmetical digression on matrices and moduli... 23
4. The Betti and torsion numbers of a complex and
their calculation 34
5. Circuits and their orientation 44
6. Orientation of Sn 54
7. Convex complexes and their subdivision. Invariance
of the homology characters under subdivision 58
CHAPTER n
TOPOLOGICAL INVARIANCE OF THE HOMOLOGY
CHARACTERS
1. Topological homology characters 72
2. Deformations. The Poincare Group 76
3. The fundamental deformation theorem for complexes 84
4. Invariance of the homology characters 87
5. Invariance under partial homeomorphism 90
6. Invariance of dimensionality, regionality and the
simple circuit 97
7. Extension of boundary relations 102
8. Combinatorial complexes 105
ix
x CONTENTS
Section Page
CHAPTER III
MANIFOLDS AND THEIR DUALITY THEOREMS
1. The structure of the stars of a normal complex .. 116
2. Definition of manifolds and their general properties 119
3. Duality relations for the homology characters .... 135
4. Invariance of manifolds 155
CHAPTER IV
INTERSECTIONS OF CHAINS ON A MANIFOLD
1. Polyhedral intersections 162
2. Special combinatorial properties of the Kronecker
index 174
3. Intersections of arbitrary chains and their com¬
binatorial invariance 182
4. Topological invariance of the intersection elements 198
5. Looping coefficients 205
6. A new definition of intersections of chains 210
7. Miscellaneous questions 216
CHAPTER V
PRODUCT COMPLEXES
1. Generalities on product sets and spaces 220
2. Product complexes 222
3. Products of manifolds 234
CHAPTER VI
TRANSFORMATIONS OF MANIFOLDS, THEm
COINCIDENCES AND FIXED POINTS
1. Position of the problem 245
2. Representative cycles of the transformations. The
signed coincidences or fixed points 247
3. Approximation to transformations of complexes ... 255
4. Transformations of the cycles 258
5. The numbers of signed coincidences and fixed points 268
6. Special properties of single valued transformations 278
7. Extension to arbitrary complexes 281
CONTENTS Xi
Section Paga
CHAPTER Vn
INFINITE COMPLEXES AND THEIR APPLICATIONS
1. General properties of infinite complexes 292
2. Ideal elements 295
3. Infinite manifolds and their duality theory 312
4. Compact metric spaces and their homology characters 323
5. Closed subsets of Sr 336
6. Transformations of compact metric spaces 343
CHAPTER VIII
APPLICATIONS TO ANALYTICAL AND
ALGEBRAIC VARIETIES
1. Analytical varieties 362
2. Intersections of analytical varieties 369
3. Complex varieties 377
4. Applications to algebraic geometry 385
Bibliography 393
Addenda 409
Index 410
|
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| indexdate | 2024-07-09T15:51:04Z |
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| language | English |
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| physical | XI, 413 S. |
| publishDate | 1965 |
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| publisher | Chelsea Publ. Co. |
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| spelling | Lefschetz, Solomon 1884-1972 Verfasser (DE-588)117714895 aut Topology 2. ed., 2. print. New York Chelsea Publ. Co. 1965 XI, 413 S. txt rdacontent n rdamedia nc rdacarrier Topologie (DE-588)4060425-1 gnd rswk-swf Topologie (DE-588)4060425-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001837786&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lefschetz, Solomon 1884-1972 Topology Topology Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4060425-1 |
| title | Topology |
| title_auth | Topology |
| title_exact_search | Topology |
| title_full | Topology |
| title_fullStr | Topology |
| title_full_unstemmed | Topology |
| title_short | Topology |
| title_sort | topology |
| topic | Topology Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topology Topologie |
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