Verfügbarkeit: 4-manifolds | Technische Universität München

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Bibliographische Detailangaben
Beteilige Person:	Akbulut, Selman 1949- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Oxford, United Kingdom Oxford University Press 2016
Ausgabe:	First edition
Schriftenreihe:	Oxford graduate texts in mathematics 25
Schlagwörter:	Mannigfaltigkeit Dimension 4
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029094833&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029094833&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	xii, 262 Seiten Illustrationen, Diagramme
ISBN:	9780198784869 0198784864

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Datensatz im Suchindex

DE-BY-UBR_call_number	8019/SK 370 A313
DE-BY-UBR_katkey	5903117
DE-BY-UBR_location	UB Handapparat Mathematik Prof. Friedl 1
DE-BY-UBR_media_number	TEMP12592986
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adam_text	Contents Preface vii 1 4-manifold handlebodies 1 1.1 Carving ............................................................ 4 1.2 Sliding handles..................................................... 6 1.3 Canceling handles................................................... 8 1.4 Carving ribbons ................................................... 10 1.5 Non-orientable handles............................................. 14 1.6 Algebraic topology................................................. 16 2 Building low-dimensional manifolds 19 2.1 Plumbing .......................................................... 21 2.2 Self plumbing...................................................... 22 2.3 Some useful diffeomorphisms........................................ 23 2.4 Examples ........................................................ 24 2.5 Constructing diffeomorphisms by carving............................ 29 2.6 Shake slice knots.................................................. 32 2.7 Some classical invariants ......................................... 33 3 Gluing 4-manifolds along their boundaries 37 3.1 Constructing -M N by the upside down method........................ 37 3.2 Constructing -M N and M(f) by the cylinder method (roping) .... 39 3.3 Codimension zero surgery M ֊ M .................................. 42 4 Bundles 43 4.1 T4 = T2xT2.................................................... 43 4.2 Cacime surface..................................................... 45 4.3 General surface bundles over surfaces.............................. 52 ix Contents 4.4 Circle bundles over 3-manifolds....................................... 52 4.5 3-manifold bundles over the circle.................................... 53 5 3-manifolds 55 5.1 Dehn surgery.......................................................... 56 5.2 From framed links to Heegaard diagrams................................ 57 5.3 Gluing knot complements............................................... 59 5.4 Carving 3-manifolds................................................... 61 5.5 Rohlin invariant ..................................................... 62 6 Operations 64 6.1 Gluck twisting ....................................................... 64 6.2 Blowing down ribbons.................................................. 67 6.3 Logarithmic transform................................................. 68 6.4 Luttinger surgery..................................................... 69 6.5 Knot surgery.......................................................... 71 6.6 Rational blowdowns.................................................... 74 7 Lefschetz fibrations 78 7.1 Elliptic surface E(n)................................................. 80 7.2 Dolgachev surfaces ................................................... 81 7.3 PALFs................................................................. 84 7.4 ALFs ................................................................. 87 7.5 BLFs ................................................................ 92 8 Symplectic manifolds 95 8.1 Contact manifolds.................................................... 96 8.2 Stein manifolds.................................................... 98 8.3 Eliashberg’s characterization of Stein............................... 99 8.4 Convex decomposition of 4-manifolds..................................101 8.5 M4 = BLF ......................................................... 103 8.6 Stein = PALF ..................................................... 106 8.7 Imbedding Stein to symplectic via PALF...............................107 8.8 Symplectic fillings..................................................109 9 Exotic 4-manifolds 112 9.1 Constructing small exotic manifolds .................................112 9.2 Iterated 0-Whitehead doubles are non-slice............................116 9.3 A solution of a conjecture of Zeeman..................................119 x Contents 9.4 An exotic R4 ........................................................119 9.5 An exotic non-orientable closed manifold ...........................120 10 Cork decomposition 123 10.1 Corks................................................................125 10.2 Anticorks .......................................................... 130 10.3 Knotting corks.......................................................132 10.4 Plugs................................................................133 11 Covering spaces 138 11.1 Handlebody of coverings .............................................138 11.2 Handlebody of branched coverings ................................... 141 11.3 Branched covers along ribbon surfaces................................147 12 Complex surfaces 150 12.1 Milnor fibers of isolated singularities..............................150 12.2 Hypersurfaces that are branched covers of CP2....................... 153 12.3 Handlebody descriptions of Vd....................................... 155 12.4 E(a,6,c).............................................................158 13 Seiberg—Witten invariants 163 13.1 Representations......................................................164 13.2 Action of A*(AT) on W± .........................................166 13.3 Dirac operator ..................................................... 171 13.4 A special calculation............................................... 173 13.5 Seiberg-Witten invariants........................................... 174 13.6 S-W when 62(A) = 1................................................. 181 13.7 Blowup formula...................................................... 182 13.8 S-W for torus surgeries............................................. 182 13.9 S-W for manifolds with T3 boundary...................................183 13.10 S-W for logarithmic transforms......................................185 13.11 S-W for knot surgery Xk............................................ 18b 13.12 S-W for S 1 x Y3....................................................189 13.13 Moduli space near the reducible solution............................191 13.14 Almost complex and symplectic structures.......................... 193 13.15 Antiholomorphic quotients...........................................200 13.16 S-W equations onRxF3................................................201 13.17 Adjunction inequality...............................................202 xi Contents 14 Some applications 206 14.1 10/8 theorem......................................................206 14.2 Cappell-Shaneson homotopy spheres.................................210 14.3 Flexible contractible 4-manifolds ................................219 14.4 Some small closed exotic manifolds................................223 14.4.1 An exotic CP2#3CP2.........................................223 14.4.2 An exotic CP2#2CP2.........................................234 14.4.3 Fintushel-Stern reverse engineering........................243 References 245 Index 261 xii 4-Manifold$ presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut. The text is aimed at graduate students and focuses on the teaching and learning of the subject, giving a direct approach to constructions and theorems which are supplemented by exercises to help the reader work through the details not covered in the proofs. Uniquely, this work contains a hundred color illustrations to demonstrate the ideas rather than providing long-winded and potentially unclear explanations. Key results have been selected that relate to the material discussed and the author has provided examples of howto analyse them with the techniques developed in earlier chapters. Selman Akbulut is a Professor at Michigan State University. His research is in topology; he has worked on topology of real algebraic sets, symplectic and G2 manifolds, and on low-dimensional manifolds with success in developing 4-dimensional handlebody techniques, settling conjectures and solving problems.
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indexdate	2024-12-20T17:42:28Z
institution	BVB
isbn	9780198784869 0198784864
language	English
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owner	DE-703 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-11
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physical	xii, 262 Seiten Illustrationen, Diagramme
publishDate	2016
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publishDateSort	2016
publisher	Oxford University Press
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series	Oxford graduate texts in mathematics
series2	Oxford graduate texts in mathematics Oxford mathematics
spellingShingle	Akbulut, Selman 1949- 4-manifolds Oxford graduate texts in mathematics Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 4 (DE-588)4338676-3 gnd
subject_GND	(DE-588)4037379-4 (DE-588)4338676-3
title	4-manifolds
title_alt	Four-manifolds
title_auth	4-manifolds
title_exact_search	4-manifolds
title_full	4-manifolds Selman Akbulut
title_fullStr	4-manifolds Selman Akbulut
title_full_unstemmed	4-manifolds Selman Akbulut
title_short	4-manifolds
title_sort	4 manifolds
topic	Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 4 (DE-588)4338676-3 gnd
topic_facet	Mannigfaltigkeit Dimension 4
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work_keys_str_mv	AT akbulutselman 4manifolds AT akbulutselman fourmanifolds

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