A combination theorem for relatively hyperbolic groups and finite relative height of splitting
Abstract
In this paper, we prove a combination theorem for a relatively acylindrical graph of relatively hyperbolic groups (Theorem 1.1). Here, we are extending the technique of [Tom21] and constructing Bowditch boundary of the fundamental group of graph of groups. Suppose G(Y) is a graph of relatively hyperbolic groups such that edge groups are relatively quasi-convex in adjacent vertex groups. Also, assume that the fundamental group of G(Y) is relatively hyperbolic. Then we show that the edge groups of G(Y) have finite relative height (Definition 1.5) if and only if they are relatively quasi-convex (Theorem 1.6). In the last section, we give an application.
Keywords
Cite
@article{arxiv.2207.03167,
title = {A combination theorem for relatively hyperbolic groups and finite relative height of splitting},
author = {Ravi Tomar},
journal= {arXiv preprint arXiv:2207.03167},
year = {2022}
}
Comments
15 pages. arXiv admin note: text overlap with arXiv:2104.08843; text overlap with arXiv:math/0203258 by other authors