# Complex of Relatively Hyperbolic Groups

## TL;DR

This paper establishes a new combination theorem for complexes of relatively hyperbolic groups, extending previous results on hyperbolic groups over simplicial complexes, thereby broadening the understanding of group combinations in geometric group theory.

## Contribution

It generalizes Martin's combination theorem from hyperbolic groups to relatively hyperbolic groups over more complex structures.

## Key findings

- Proves a combination theorem for complexes of relatively hyperbolic groups
- Extends existing hyperbolic group combination results to a broader class
- Provides a framework for analyzing group structures over complex simplicial complexes

## Abstract

In this article, we prove a combination theorem for a complex of relatively hyperbolic groups. It is a generalization of Martin's \cite{martin} work for combination of hyperbolic groups over a finite $M_K$-simplicial complex, where $k\leq 0$.