Rigidity of high dimensional graph manifolds:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Paris
Société Mathématique de France
2015
|
| Series: | Astérisque
372 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 177 Seiten |
| ISBN: | 9782856298091 |
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Record in the Search Index
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| adam_text | Titel: Rigidity of high dimensional graph manifolds
Autor: Frigerio, Roberto
Jahr: 2015
CONTENTS Introduction xi Part I. Graph manifolds: topological and algebraic properties ................................................ 1 1. Quasi-isometries and quasi-actions ................................. .3 1.1. The quasi-isometry lype of a group ................................. . i 1.2. The Milnor-Svarz Lemma ........................................... 1 1.3. From quasi-isomet ries t o quasi-aet ions .............................. 1 2. Generalized graph manifolds ........................................ 9 2.1. Putting a. metric on (extended) graph manifolds .................... 11 2.2. Purely hyperbolic graph manifolds are nonposit ively curved ........ 12 2.3. 7Ti (A/ ) as lh( fundament al group of a graph of groups .............. 11 2.1. The univ( rsal cover of M as a tree of spaces ........................ la 2.3. Basic metric proper!ies of M ........................................ 18 2.(i. Kxamples not support ing any locally CAT(ll) nu t ric ................ 19 3. Topological rigidity ................................................... 23 3.1. ( out rael ible universal cover ......................................... 21 .3.2. Lower algebraic K-t henry ........................................... 28 3.3. Topological rigidity - t lie general case ............................... 27 3.1. Topological rigidity - (extended) graph manifolds ................... 31 3.8. Hau 111 -( mines ( onjeet lire and consequences ......................... 32 4. Isomorphisms preserve piece s ................. 1.1. Some proper! ies ol wall stabilizers ............ 1.2. ( harael erizing surface pieces .................. 1.3. Purl her proper! ies of wall stabilizers .......... I. 1. Isomorphisms quasi-preserve non-surface pieces 1.8. Isomorphisms preserve pieces ................. • - ) .3(1 38 It) 12 5. Smooth rigidity ............. 8.1. Itigidlv decomposable pairs 8.2. I )elm t wist s ............... 17
CONTKNTS Proof of TI ioitrom 5.4 4. I, Mapping, class group G. Algebraic properties .................................................. 57 G.l. (iraplis of groups and groups act ing oil t roes ........................ 58 G.2. The graph of groups associated to au (extended) graph manifold . . . (it) G.T Relative hyperbolieity and hyperbolieally embedded subgroups ..... fit) G. 1. Kazhdan subgroups .................... ............................. G7 G.5. 1 uiiforinlv exponent ial growt h ....................................... G8 (i.G. The Tits Alternat ive ................................................ G!) G.7. ( o-I lopl properly ................................................... t- G.S. ( -simplicity of aeylindrieal graphs of groups ....................... 75 G.T SQ-imiversalily ..................................................... 78 (i.lt). Solvable word problem ............................................. 7!) G. I I. (linings and isomorphism type ..................................... 84 Part II. Irreducible graph manifolds: coarse geometric properties 7. Irreducible graph manifolds ......................................... 7.1. I he geomei ry ol chambers and walls ................................ 7.2. An important consequence of irredueibility .......................... 7.4. 1 he geometry ol neutered spaces .................................... 7. I. Walls and chambers are quasi-isomet rically embedded in the universal covering of irreducible graph manifolds ............................ 8. Pieces of irreducible graph manifolds are quasi-preserved ....... s. I . 1 he asymptotic cone ol a geodesic metric space ..................... s.2. Quasi-isometries and asymptotic coin s .............................. s.4, I roe-graded spaces .................................................. s. 1. 1 he asylitpt ol ic cone of .1 / .......................................... s.4 A charact eri/al ion ol b i- 1 .ipsehit z (u
I (-flats in 4T................ s ti A cliaraci I ri/al ion ol quasi-Hats ol maximal dimension in M ........ s i Walls a i id chambers are 11 nisi - present d bv |uasi-isonict ries ........ ueknos.s and n laI ive hviicrbiilicit v 01 04 0-1 05 0G 00 100 100 1 24 12 I 1 25 0. Quasi isometry rigidity. I ............................................ 120 o.l. I lie ( 111 a S i - a c t ioi I of b on .1 / ......................................... 140 0 2. The image of U ...................................................... 142 0.4. I la la a i n -1 o| n ...................................................... 14 1 0 1 Abi hai; 1 11 id M i il ei | normal subgroups are virtually central ......... 14G o.- 1 Piece- with quasi isometric f 111 1 d a ni c 11 1 a I groups ..................... 140 It). Quasi isometry rigidity. II ID a c I i o 1 1 - 1 1 ] actions
(’ONTKNTS ix 10.2. Tin- action of l’ n on 7’ ............................................. 1 12 10.0. Stabilizers of edges and vortices .................................... 1 10 10. 1. Graph manifolds with quasi-isonict rio fnndanK iit al groups ......... Ill Part III. Concluding remarks ......................................... 1 17 11. Examples not supporting locally CAT(O) metrics ............... 1 10 11.1. Fiber bundles ...................................................... 119 11.2. Irreducible examples ............................................... 100 12. Directions for future research ..................................... Mid 12.1. Furt her algebraic properties ........................................ Kid 12.2. St tidying quasi-isomet ries .......................................... Iti I 12.0. Xon-posit ivo curvature and differential geometry .................. Ititi Bibliography .............................................................. KiO
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| any_adam_object | 1 |
| author | Frigerio, Roberto 1977- Lafont, Jean-François Sisto, Alessandro |
| author_GND | (DE-588)1081148209 (DE-588)108048955X (DE-588)1080490957 |
| author_facet | Frigerio, Roberto 1977- Lafont, Jean-François Sisto, Alessandro |
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| indexdate | 2024-07-10T07:21:01Z |
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| isbn | 9782856298091 |
| language | English |
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| physical | XXI, 177 Seiten |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Société Mathématique de France |
| record_format | marc |
| series | Astérisque |
| series2 | Astérisque |
| spelling | Frigerio, Roberto 1977- Verfasser (DE-588)1081148209 aut Rigidity of high dimensional graph manifolds Roberto Frigerio, Jean-François Lafont, Alessandro Sisto Paris Société Mathématique de France 2015 XXI, 177 Seiten txt rdacontent n rdamedia nc rdacarrier Astérisque 372 Lafont, Jean-François (DE-588)108048955X aut Sisto, Alessandro (DE-588)1080490957 aut Astérisque 372 (DE-604)BV002579439 372 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028649196&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Frigerio, Roberto 1977- Lafont, Jean-François Sisto, Alessandro Rigidity of high dimensional graph manifolds Astérisque |
| title | Rigidity of high dimensional graph manifolds |
| title_auth | Rigidity of high dimensional graph manifolds |
| title_exact_search | Rigidity of high dimensional graph manifolds |
| title_full | Rigidity of high dimensional graph manifolds Roberto Frigerio, Jean-François Lafont, Alessandro Sisto |
| title_fullStr | Rigidity of high dimensional graph manifolds Roberto Frigerio, Jean-François Lafont, Alessandro Sisto |
| title_full_unstemmed | Rigidity of high dimensional graph manifolds Roberto Frigerio, Jean-François Lafont, Alessandro Sisto |
| title_short | Rigidity of high dimensional graph manifolds |
| title_sort | rigidity of high dimensional graph manifolds |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028649196&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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