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Table of Contents:

Chapter 1: Introduction
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Research Questions
1.4 Significance of the Study
1.5 Definition of Terms

Chapter 2: Literature Review
2.1 Overview of Geometric Group Theory
2.2 Basics of Hyperbolic Spaces
2.3 Previous Studies on Geometric Group Theory and Hyperbolic Spaces

Chapter 3: Research Methodology
3.1 Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques

Chapter 4: Discussion of Findings
4.1 Analysis of Results
4.2 Comparison with Previous Studies
4.3 Implications of Findings

Chapter 5: Conclusion and Summary
5.1 Summary of Findings
5.2 Conclusion
5.3 Recommendations for Future Research

Brief Overview:

Geometric group theory is a branch of mathematics that studies finitely generated groups as geometric objects and explores the connections between their algebraic and geometric properties. Hyperbolic spaces, on the other hand, are geometric spaces with negative curvature and have been studied extensively in mathematics and theoretical physics.

The thesis on Geometric Group Theory and Hyperbolic Spaces aims to explore the relationship between these two areas of study and investigate how geometric properties of groups can be characterized using hyperbolic spaces. The research will involve a literature review of previous studies in the field, followed by a detailed analysis of the methodology used to conduct the study.

The findings of the research will be discussed in Chapter 4, where the results will be analyzed and compared with previous studies. The implications of the findings will also be explored, along with recommendations for future research in the field.

In conclusion, the thesis on Geometric Group Theory and Hyperbolic Spaces will contribute to the existing body of knowledge on these topics and provide valuable insights for researchers and mathematicians interested in the intersection of algebra and geometry.

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