The group fixed by a family of injective endomorphisms of a free group:
This monograph contains a proof of the Bestvina-Handel Theorem (for any automorphism of a free group of rank n, the fixed group has rank at most n) that to date has not been available in book form. The account is self-contained, simplified, purely algebraic, and extends the results to an arbitrary f...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1996
|
| Schriftenreihe: | Contemporary mathematics
195 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This monograph contains a proof of the Bestvina-Handel Theorem (for any automorphism of a free group of rank n, the fixed group has rank at most n) that to date has not been available in book form. The account is self-contained, simplified, purely algebraic, and extends the results to an arbitrary family of injective endomorphisms. The topological proof by Bestvina-Handel is translated into the language of groupoids and many details previously left to the reader are meticulously verified in this text. |
| Beschreibung: | 81 S. graph. Darst. |
| ISBN: | 0821805649 |
Internformat
MARC
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| 100 | 1 | |a Dicks, Warren |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The group fixed by a family of injective endomorphisms of a free group |c Warren Dicks ; Enric Ventura |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1996 | |
| 300 | |a 81 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Contemporary mathematics |v 195 | |
| 520 | 3 | |a This monograph contains a proof of the Bestvina-Handel Theorem (for any automorphism of a free group of rank n, the fixed group has rank at most n) that to date has not been available in book form. The account is self-contained, simplified, purely algebraic, and extends the results to an arbitrary family of injective endomorphisms. The topological proof by Bestvina-Handel is translated into the language of groupoids and many details previously left to the reader are meticulously verified in this text. | |
| 650 | 7 | |a Automorfismen |2 gtt | |
| 650 | 4 | |a Automorphismes | |
| 650 | 7 | |a Automorphismes |2 ram | |
| 650 | 4 | |a Groupes métabéliens libres | |
| 650 | 7 | |a Groupes métabéliens libres |2 ram | |
| 650 | 7 | |a Groupoids |2 gtt | |
| 650 | 4 | |a Groupoïdes | |
| 650 | 7 | |a Groupoïdes |2 ram | |
| 650 | 4 | |a Automorphisms | |
| 650 | 4 | |a Free metabelian groups | |
| 650 | 4 | |a Groupoids | |
| 650 | 0 | 7 | |a Metabelsche Gruppe |0 (DE-588)4287358-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Automorphismus |0 (DE-588)4143709-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Freie Gruppe |0 (DE-588)4155283-0 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Ventura, Enric |d 1965- |e Verfasser |0 (DE-588)1160727015 |4 aut | |
| 830 | 0 | |a Contemporary mathematics |v 195 |w (DE-604)BV000003365 |9 195 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-007254786 | ||
Datensatz im Suchindex
| _version_ | 1804125339750760448 |
|---|---|
| adam_text | Contents
Introduction 1
Chapter I. Groupoids 5
1.1. Abstract Maps of Graphs 5
1.2. The Basic Operations 11
1.3. Free Groupoids 14
1.4. Inertia 18
1.5. The Fixed Subgroupoid 23
Chapter II. Measuring Devices 27
II. 1. Some Aspects of the Perron Frobenius Theorem 27
11.2. Metric Graphs and Weighted Graphs 30
11.3. The Five Quantifiers 33
Chapter III. Properties of the Basic Operations 35
111.1. Collapsing a Pretrivial Arc 35
111.2. Subdividing 36
111.3. Folding 39
111.4. Removing a Vertex of Valence Two 42
Chapter IV. Minimal Representatives and Fixed Subgroupoids 45
IV. 1. Existence 45
IV.2. Smoothness 47
IV.3. Indivisible Fixed Elements 51
IV.4. Folding Indivisible Fixed Elements 55
IV.5. Inertia of the Fixed Subgroupoid 61
Open Problems 71
Bibliography 75
Index 77
be
|
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| author | Dicks, Warren Ventura, Enric 1965- |
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| classification_rvk | SK 260 SI 805 |
| ctrlnum | (OCoLC)34356049 (DE-599)BVBBV010852967 |
| dewey-full | 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010852967 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:00:00Z |
| institution | BVB |
| isbn | 0821805649 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007254786 |
| oclc_num | 34356049 |
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| owner_facet | DE-12 DE-739 DE-188 |
| physical | 81 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Contemporary mathematics |
| series2 | Contemporary mathematics |
| spelling | Dicks, Warren Verfasser aut The group fixed by a family of injective endomorphisms of a free group Warren Dicks ; Enric Ventura Providence, RI American Math. Soc. 1996 81 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Contemporary mathematics 195 This monograph contains a proof of the Bestvina-Handel Theorem (for any automorphism of a free group of rank n, the fixed group has rank at most n) that to date has not been available in book form. The account is self-contained, simplified, purely algebraic, and extends the results to an arbitrary family of injective endomorphisms. The topological proof by Bestvina-Handel is translated into the language of groupoids and many details previously left to the reader are meticulously verified in this text. Automorfismen gtt Automorphismes Automorphismes ram Groupes métabéliens libres Groupes métabéliens libres ram Groupoids gtt Groupoïdes Groupoïdes ram Automorphisms Free metabelian groups Groupoids Metabelsche Gruppe (DE-588)4287358-7 gnd rswk-swf Automorphismus (DE-588)4143709-3 gnd rswk-swf Freie Gruppe (DE-588)4155283-0 gnd rswk-swf Metabelsche Gruppe (DE-588)4287358-7 s Freie Gruppe (DE-588)4155283-0 s Automorphismus (DE-588)4143709-3 s DE-604 Ventura, Enric 1965- Verfasser (DE-588)1160727015 aut Contemporary mathematics 195 (DE-604)BV000003365 195 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007254786&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dicks, Warren Ventura, Enric 1965- The group fixed by a family of injective endomorphisms of a free group Contemporary mathematics Automorfismen gtt Automorphismes Automorphismes ram Groupes métabéliens libres Groupes métabéliens libres ram Groupoids gtt Groupoïdes Groupoïdes ram Automorphisms Free metabelian groups Groupoids Metabelsche Gruppe (DE-588)4287358-7 gnd Automorphismus (DE-588)4143709-3 gnd Freie Gruppe (DE-588)4155283-0 gnd |
| subject_GND | (DE-588)4287358-7 (DE-588)4143709-3 (DE-588)4155283-0 |
| title | The group fixed by a family of injective endomorphisms of a free group |
| title_auth | The group fixed by a family of injective endomorphisms of a free group |
| title_exact_search | The group fixed by a family of injective endomorphisms of a free group |
| title_full | The group fixed by a family of injective endomorphisms of a free group Warren Dicks ; Enric Ventura |
| title_fullStr | The group fixed by a family of injective endomorphisms of a free group Warren Dicks ; Enric Ventura |
| title_full_unstemmed | The group fixed by a family of injective endomorphisms of a free group Warren Dicks ; Enric Ventura |
| title_short | The group fixed by a family of injective endomorphisms of a free group |
| title_sort | the group fixed by a family of injective endomorphisms of a free group |
| topic | Automorfismen gtt Automorphismes Automorphismes ram Groupes métabéliens libres Groupes métabéliens libres ram Groupoids gtt Groupoïdes Groupoïdes ram Automorphisms Free metabelian groups Groupoids Metabelsche Gruppe (DE-588)4287358-7 gnd Automorphismus (DE-588)4143709-3 gnd Freie Gruppe (DE-588)4155283-0 gnd |
| topic_facet | Automorfismen Automorphismes Groupes métabéliens libres Groupoids Groupoïdes Automorphisms Free metabelian groups Metabelsche Gruppe Automorphismus Freie Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007254786&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003365 |
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