Algebraic topology of finite topological spaces and applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Schriftenreihe: | Lecture notes in mathematics
2032 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVII, 170 S. graph. Darst. |
| ISBN: | 3642220029 9783642220029 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1805144995496198144 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
PRELIMINARIES 1
1.1 FINITE SPACES AND POSETS 2
1.2 MAPS, HOMOTOPIES AND CONNECTEDNESS 4
1.3 HOMOTOPY TYPES 6
1.4 WEAK HOMOTOPY TYPES: THE THEORY OF MCCORD. 10
BASIC TOPOLOGICAL PROPERTIES OF FINITE SPACES 19
2.1 HOMOTOPY AND CONTIGUITY 19
2.2 MINIMAL PAIRS 20
2.3 TI-SPACES 22
2.4 LOOPS IN THE HASSE DIAGRAM AND THE FUNDAMENTAL GROUP 22 2.5 EULER
CHARACTERISTIC 25
2.6 AUTOMORPHISM GROUPS OF FINITE POSETS 27
2.7 JOINS, PRODUCTS, QUOTIENTS AND WEDGES 29
2.8 A FINITE ANALOGUE OF THE MAPPING CYLINDER 34
MINIMAL FINITE MODELS 37
3.1 A FINITE SPACE APPROXIMATION 37
3.2 MINIMAL FINITE MODELS OF THE SPHERES 39
3.3 MINIMAL FINITE MODELS OF GRAPHS 40
3.4 THE/PO 44
SIMPLE HOMOTOPY TYPES AND FINITE SPACES 49
4.1 WHITEHEAD'S SIMPLE HOMOTOPY TYPES 50
4.2 SIMPLE HOMOTOPY TYPES: THE FIRST MAIN THEOREM 53
4.3 JOINS, PRODUCTS, WEDGES AND COLLAPSIBILITY 60
4.4 SIMPLE HOMOTOPY EQUIVALENCES: THE SECOND MAIN THEOREM 64
4.5 A SIMPLE HOMOTOPY VERSION OF QUILLEN'S THEOREM A 68 4.6 SIMPLE,
STRONG AND WEAK HOMOTOPY IN TWO STEPS 70
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1011959372
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
5 STRANG HOMOTOPY TYPES 73
5.1 A SIMPLICIAL NOTION OF HOMOTOPY 73
5.2 RELATIONSHIP WITH FINITE SPACES AND BARYCENTRIC SUBDIVISIONS 77
5.3 NERVES OF COVERS AND THE NERVE OF A COMPLEX 80
6 METHODS OF REDUCTION 85
6.1 OSAKI'S REDUCTION METHODS 85
6.2 7-POINTS AND ONE-POINT REDUCTION METHODS 87
7 H-REGULAR COMPLEXES AND QUOTIENTS 93
7.1 H-REGULAR CW-COMPLEXES AND THEIR ASSOCIATED FINITE SPACES 93
7.2 QUOTIENTS OF FINITE SPACES: AN EXACT SEQUENCE FOR HOMOLOGY GROUPS
100
8 GROUP ACTIONS AND A CONJECTURE OF QUILLEN 105
8.1 EQUIVARIANT HOMOTOPY THEORY FOR FINITE SPACES 106
8.2 THE POSET OF NONTRIVIAL P-SUBGROUPS AND THE CONJECTURE OF QUILLEN
108
8.3 EQUIVARIANT SIMPLE HOMOTOPY TYPES I LL
8.4 APPLICATIONS TO QUILLEN'S WORK 119
9 REDUCED LATTICES 121
9.1 THE HOMOTOPY OF REDUCED LATTICES 121
9.2 T H E COMPLEX 124
10 FIXED POINTS AND THE LEFSCHETZ NUMBER 129
10.1 THE FIXED POINT PROPERTY FOR FINITE SPACES 129
10.2 ON THE LEFSCHETZ THEOREM FOR SIMPLICIAL AUTOMORPHISMS 133
11 THE ANDREWS-CURTIS CONJECTURE 137
11.1 N-DEFORMATIONS AND STATEMENTS OF THE CONJECTURES 137 11.2 QUASI
CONSTRUCTIBLE COMPLEXES 139
11.3 THE DUAL NOTION OF QUASI CONSTRUCTIBILITY 145
12 APPENDIX 151
A .I SIMPLICIAL COMPLEXES 151
A.2 CW-COMPLEXES AND A GLUING THEOREM 155
REFERENCES 161
LIST OF SYMBOLS 165
INDEX 167 |
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| author | Barmak, Jonathan A. |
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| author_facet | Barmak, Jonathan A. |
| author_role | aut |
| author_sort | Barmak, Jonathan A. |
| author_variant | j a b ja jab |
| building | Verbundindex |
| bvnumber | BV039526795 |
| classification_rvk | SI 850 |
| classification_tum | MAT 550f |
| ctrlnum | (OCoLC)750826622 (DE-599)DNB1011959372 |
| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2 |
| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-21T00:06:59Z |
| institution | BVB |
| isbn | 3642220029 9783642220029 |
| language | English |
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| physical | XVII, 170 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Barmak, Jonathan A. Verfasser (DE-588)1015078419 aut Algebraic topology of finite topological spaces and applications Jonathan A. Barmak Berlin [u.a.] Springer 2011 XVII, 170 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2032 Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 s Algebraische Topologie (DE-588)4120861-4 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-22003-6 Lecture notes in mathematics 2032 (DE-604)BV000676446 2032 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3826587&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024379160&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barmak, Jonathan A. Algebraic topology of finite topological spaces and applications Lecture notes in mathematics Algebraische Topologie (DE-588)4120861-4 gnd Topologischer Raum (DE-588)4137586-5 gnd |
| subject_GND | (DE-588)4120861-4 (DE-588)4137586-5 |
| title | Algebraic topology of finite topological spaces and applications |
| title_auth | Algebraic topology of finite topological spaces and applications |
| title_exact_search | Algebraic topology of finite topological spaces and applications |
| title_full | Algebraic topology of finite topological spaces and applications Jonathan A. Barmak |
| title_fullStr | Algebraic topology of finite topological spaces and applications Jonathan A. Barmak |
| title_full_unstemmed | Algebraic topology of finite topological spaces and applications Jonathan A. Barmak |
| title_short | Algebraic topology of finite topological spaces and applications |
| title_sort | algebraic topology of finite topological spaces and applications |
| topic | Algebraische Topologie (DE-588)4120861-4 gnd Topologischer Raum (DE-588)4137586-5 gnd |
| topic_facet | Algebraische Topologie Topologischer Raum |
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| volume_link | (DE-604)BV000676446 |
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