Blowups, slicings and permutation groups in combinatorial topology:
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| Main Author: | |
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| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin
Logos-Verl.
2011
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | 250 S. graph. Darst. 21 cm |
| ISBN: | 9783832529833 3832529837 |
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Record in the Search Index
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| adam_text |
IMAGE 1
CONTENTS
ZUSAMMENFASSUNG 19
PREFACE 23
1 INTRODUCTION AND RESULTS 27
1.1 POLYTOPES AND SIMPLICIAL COMPLEXES 27
1.2 SIMPLICIAL (CO-)HOMOLOGY 29
1.3 LOWER AND UPPER BOUND THEOREMS 34
1.4 3-MANIFOLDS AND NORMAL SURFACES 38
1.5 SIMPLY CONNECTED 4-MANIFOLDS 43
1.6 DISCRETE MORSE THEORY AND SLICINGS 47
1.7 BISTCLLAR MOVES 50
1.8 RESULTS 52
2 COMBINATORIAL BLOWUPS 55
2.1 INTRODUCTION 55
2.2 THE KUMMER VARIETY AND THE K3 SURFACE 57
2.3 THE HOPF CR-PROCCSS 59
2.4 AN ALTERNATIVE CONSTRUCTION OF THE K3 SURFACE 61
2.4.1 A TRIANGULATED MAPPING CYLINDER 61
2.4.2 SIMPLICIAL BLOWUPS 66
2.5 OTHER SIMPLY CONNECTED COMBINATORIAL 4-MANIFOLDS 68
2.6 RESOLUTION OF OTHER TYPES OF SINGULARITIES 71
3 SLICINGS AND DISCRETE NORMAL SURFACES 73
3.1 INTRODUCTION 73
3.2 THE GENUS OF DISCRETE NORMAL SURFACES 74
5
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1016011938
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
3.3 THE COMBINATORIAL STRUCTURE OF SLICINGS 79
3.4 BISTELLAR MOVES IN SLICINGS 82
3.5 TRIANGLES VS. QUADRILATERALS 86
3.6 WEAKLY NEIGHBORLY SLICINGS 94
3.7 SLICINGS AND CRITICAL POINT THEORY IN HIGHER DIMENSIONS 99
4 SIMPLY TRANSITIVE COMBINATORIAL 2- A ND 3-MANIFOIDS 107
4.1 INTRODUCTION 107
4.2 SURFACES AS SUBCOMPLEXES OF REGULAR POLYTOPES 112
4.3 THE DECOMPOSITION OF THE 2-SKELETON OF SS K 115
4.4 THE DECOMPOSITION OF THE 2-SKELETON OF A*" 1 121
4.5 TRANSITIVE 3-DIMENSIONAL COMBINATORIAL MANIFOLDS 127
4.5.1 THE SERIES LE* 129
4.5.2 THE SERIES KU 4N 131
4.5.3 THE SERIES C 2N AND D2N 133
4.5.4 OVERVIEW AND FURTHER SERIES 138
4.5.5 THREE CONJECTURED SERIES OF NEIGHBORLY SPHERE BUNDLES 144
5 DOUBLY TRANSITIVE COMBINATORIAL (PSEUDO-)MANIFOLDS 149
5.1 INTRODUCTION 149
5.2 MULTIPLY TRANSITIVE "PINCH POINT" SURFACES 152
5.3 MULTIPLY TRANSITIVE COMBINATORIAL 3-MANIFOLDS 156
5.4 A 3-TRANSITIVE COMBINATORIAL 3-PSEUDOMANIFOLD 157
5.5 2-TRANSITIVE COMBINATORIAL 3-PSEUDOMANIFOLDS 158
5.6 THE 4-DIMENSIONAL CASE 161
5.7 2-TRANSITIVE 3-NEIGHBORLY 4-MANIFOLDS 162
5.8 SHARPLY 2-TRANSITIVE COMBINATORIAL 4-PSEUDOMANIFOLDS 167
5.9 SUMMARY 178
APPENDICES
A SIMPCOMP - A GAP TOOLBOX FOR SIMPLICIAL COMPLEXES 181
A.I WHY SIMPCOMP 182
A.2 SIMPCOMP BENEFITS 182
6
IMAGE 3
CONTENTS
A.3 SOME OPERATIONS AND CONSTRUCTIONS 183
A.4 EXAMPLES 184
A.4.1 4-MANIFOLDS 184
A.4.2 THE CLASSIFICATION OF TRANSITIVE COMBINATORIAL MANIFOLDS 186
A.4.3 BISTELLAR MOVES 187
A.4.4 SIMPLICIAL BLOWUPS 188
A.4.5 HANDLCBODIES AND COLLAPSING 189
A.4.6 SLICINGS 189
A.4.7 FUNDAMENTAL GROUP AND DOUBLE SUSPENSION 190
B THE BLOWUP PROCESS, STEP BY STEP 191
C A NON-SIMPLY CONNECTED COMBINATORIAL 4-MANIFOLD 221
D SERIES OF CYCLIC COMBINATORIAL 3-MANIFOLDS 229
BIBLIOGRAPHY 235
INDEX 243 |
| any_adam_object | 1 |
| author | Spreer, Jonathan |
| author_GND | (DE-588)1016968884 |
| author_facet | Spreer, Jonathan |
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| author_variant | j s js |
| building | Verbundindex |
| bvnumber | BV041887567 |
| classification_rvk | SK 280 |
| ctrlnum | (OCoLC)767912176 (DE-599)DNB1016011938 |
| dewey-full | 514.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.22 |
| dewey-search | 514.22 |
| dewey-sort | 3514.22 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| spelling | Spreer, Jonathan Verfasser (DE-588)1016968884 aut Blowups, slicings and permutation groups in combinatorial topology vorgelegt von Jonathan Spreer Berlin Logos-Verl. 2011 250 S. graph. Darst. 21 cm txt rdacontent n rdamedia nc rdacarrier Zugl.: Stuttgart, Univ., Diss., 2011 Permutationsgruppe (DE-588)4173833-0 gnd rswk-swf Simplizialer Komplex (DE-588)4181492-7 gnd rswk-swf Aufblasung (DE-588)4139570-0 gnd rswk-swf Kombinatorische Topologie (DE-588)4137530-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kombinatorische Topologie (DE-588)4137530-0 s Aufblasung (DE-588)4139570-0 s Simplizialer Komplex (DE-588)4181492-7 s Permutationsgruppe (DE-588)4173833-0 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3895994&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=027331554&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Spreer, Jonathan Blowups, slicings and permutation groups in combinatorial topology Permutationsgruppe (DE-588)4173833-0 gnd Simplizialer Komplex (DE-588)4181492-7 gnd Aufblasung (DE-588)4139570-0 gnd Kombinatorische Topologie (DE-588)4137530-0 gnd |
| subject_GND | (DE-588)4173833-0 (DE-588)4181492-7 (DE-588)4139570-0 (DE-588)4137530-0 (DE-588)4113937-9 |
| title | Blowups, slicings and permutation groups in combinatorial topology |
| title_auth | Blowups, slicings and permutation groups in combinatorial topology |
| title_exact_search | Blowups, slicings and permutation groups in combinatorial topology |
| title_full | Blowups, slicings and permutation groups in combinatorial topology vorgelegt von Jonathan Spreer |
| title_fullStr | Blowups, slicings and permutation groups in combinatorial topology vorgelegt von Jonathan Spreer |
| title_full_unstemmed | Blowups, slicings and permutation groups in combinatorial topology vorgelegt von Jonathan Spreer |
| title_short | Blowups, slicings and permutation groups in combinatorial topology |
| title_sort | blowups slicings and permutation groups in combinatorial topology |
| topic | Permutationsgruppe (DE-588)4173833-0 gnd Simplizialer Komplex (DE-588)4181492-7 gnd Aufblasung (DE-588)4139570-0 gnd Kombinatorische Topologie (DE-588)4137530-0 gnd |
| topic_facet | Permutationsgruppe Simplizialer Komplex Aufblasung Kombinatorische Topologie Hochschulschrift |
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| work_keys_str_mv | AT spreerjonathan blowupsslicingsandpermutationgroupsincombinatorialtopology |