Kenison, George and Sharp, Richard (2017) Orbit counting in conjugacy classes for free groups acting on trees. Journal of Topology and Analysis, 9 (4). pp. 631-647. doi:10.1142/S1793525317500261

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Abstract

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Conjugacy classes, Free groups, Graph theory, Geodesics (Mathematics), Matrices, Manifolds (Mathematics), Fuchsian groups
Journal or Publication Title:	Journal of Topology and Analysis
Publisher:	World Scientific Publishing Co. Pte. Ltd.
ISSN:	1793-7167
Official Date:	December 2017
Dates:	Date Event December 2017 Published 4 August 2016 Available 6 July 2016 Accepted
Volume:	9
Number:	4
Page Range:	pp. 631-647
DOI:	10.1142/S1793525317500261
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Related URLs:	Publisher

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