Nielsen realization by gluing: limit groups and free products
We generalize the Karrass–Pietrowski–Solitar and the Nielsen realization theorems from the setting of free groups to that of free products. As a result, we obtain a fixed point theorem for finite groups of outer automorphisms acting on the relative free splitting complex of Handel and Mosher and on...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
Project Euclid
2018
|
| _version_ | 1797106182641418240 |
|---|---|
| author | Hensel, S Kielak, D |
| author_facet | Hensel, S Kielak, D |
| author_sort | Hensel, S |
| collection | OXFORD |
| description | We generalize the Karrass–Pietrowski–Solitar and the Nielsen realization theorems from the setting of free groups to that of free products. As a result, we obtain a fixed point theorem for finite groups of outer automorphisms acting on the relative free splitting complex of Handel and Mosher and on the outer space of a free product of Guirardel and Levitt, and also a relative version of the Nielsen realization theorem, which, in the case of free groups, answers a question of Karen Vogtmann. We also prove Nielsen realization for limit groups and, as a byproduct, obtain a new proof that limit groups are CAT(
0
).
The proofs rely on a new version of Stallings’ theorem on groups with at least two ends, in which some control over the behavior of virtual free factors is gained. |
| first_indexed | 2024-03-07T06:58:06Z |
| format | Journal article |
| id | oxford-uuid:fed17e66-bf0b-484c-b56b-13eb4975ec88 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:58:06Z |
| publishDate | 2018 |
| publisher | Project Euclid |
| record_format | dspace |
| spelling | oxford-uuid:fed17e66-bf0b-484c-b56b-13eb4975ec882022-03-27T13:39:37ZNielsen realization by gluing: limit groups and free productsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fed17e66-bf0b-484c-b56b-13eb4975ec88EnglishSymplectic ElementsProject Euclid2018Hensel, SKielak, DWe generalize the Karrass–Pietrowski–Solitar and the Nielsen realization theorems from the setting of free groups to that of free products. As a result, we obtain a fixed point theorem for finite groups of outer automorphisms acting on the relative free splitting complex of Handel and Mosher and on the outer space of a free product of Guirardel and Levitt, and also a relative version of the Nielsen realization theorem, which, in the case of free groups, answers a question of Karen Vogtmann. We also prove Nielsen realization for limit groups and, as a byproduct, obtain a new proof that limit groups are CAT( 0 ). The proofs rely on a new version of Stallings’ theorem on groups with at least two ends, in which some control over the behavior of virtual free factors is gained. |
| spellingShingle | Hensel, S Kielak, D Nielsen realization by gluing: limit groups and free products |
| title | Nielsen realization by gluing: limit groups and free products |
| title_full | Nielsen realization by gluing: limit groups and free products |
| title_fullStr | Nielsen realization by gluing: limit groups and free products |
| title_full_unstemmed | Nielsen realization by gluing: limit groups and free products |
| title_short | Nielsen realization by gluing: limit groups and free products |
| title_sort | nielsen realization by gluing limit groups and free products |
| work_keys_str_mv | AT hensels nielsenrealizationbygluinglimitgroupsandfreeproducts AT kielakd nielsenrealizationbygluinglimitgroupsandfreeproducts |