Orbit counting in conjugacy classes for free groups acting on trees
In this paper we study the action of the fundamental group of a finite metric graph on its universal covering tree. We assume the graph is finite, connected and the degree of each vertex is at least three. Further, we assume an irrationality condition on the edge lengths. We obtain an asymptotic for...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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World Scientific Publishing
2016
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| _version_ | 1826260752784162816 |
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| author | Kenison, G Sharp, R |
| author_facet | Kenison, G Sharp, R |
| author_sort | Kenison, G |
| collection | OXFORD |
| description | In this paper we study the action of the fundamental group of a finite metric graph on its universal covering tree. We assume the graph is finite, connected and the degree of each vertex is at least three. Further, we assume an irrationality condition on the edge lengths. We obtain an asymptotic for the number of elements in a fixed conjugacy class for which the associated displacement of a given base vertex in the universal covering tree is at most T. Under a mild extra assumption we also obtain a polynomial error term. |
| first_indexed | 2024-03-06T19:10:41Z |
| format | Journal article |
| id | oxford-uuid:16aaf39c-9296-4cee-a4b8-2b5769a8cdb9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:10:41Z |
| publishDate | 2016 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | oxford-uuid:16aaf39c-9296-4cee-a4b8-2b5769a8cdb92022-03-26T10:32:38ZOrbit counting in conjugacy classes for free groups acting on treesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:16aaf39c-9296-4cee-a4b8-2b5769a8cdb9EnglishSymplectic Elements at OxfordWorld Scientific Publishing2016Kenison, GSharp, RIn this paper we study the action of the fundamental group of a finite metric graph on its universal covering tree. We assume the graph is finite, connected and the degree of each vertex is at least three. Further, we assume an irrationality condition on the edge lengths. We obtain an asymptotic for the number of elements in a fixed conjugacy class for which the associated displacement of a given base vertex in the universal covering tree is at most T. Under a mild extra assumption we also obtain a polynomial error term. |
| spellingShingle | Kenison, G Sharp, R Orbit counting in conjugacy classes for free groups acting on trees |
| title | Orbit counting in conjugacy classes for free groups acting on trees |
| title_full | Orbit counting in conjugacy classes for free groups acting on trees |
| title_fullStr | Orbit counting in conjugacy classes for free groups acting on trees |
| title_full_unstemmed | Orbit counting in conjugacy classes for free groups acting on trees |
| title_short | Orbit counting in conjugacy classes for free groups acting on trees |
| title_sort | orbit counting in conjugacy classes for free groups acting on trees |
| work_keys_str_mv | AT kenisong orbitcountinginconjugacyclassesforfreegroupsactingontrees AT sharpr orbitcountinginconjugacyclassesforfreegroupsactingontrees |