2006/07/01 by Brian H. Bowditch · 2 citations
Mathematics · #Algebra over a field #Calculus (dental) #Computer science #Exposition (narrative) #Finite Group Theory Research #Geometric and Algebraic Topology #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Library science #Mathematics #Mathematics education #Presentation (obstetrics) #Pure mathematics #Subject (documents)
paper · doi:10.1142/e003
openalex publication_date 2006/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
These notes are based on a series of lectures I gave at the Tokyo Institute of Technology from April to July 2005. They constituted a course entitled “An introduction to geometric group theory ” totalling about 20 hours. The audience consisted of fourth year students, graduate students as well as several staff members. I therefore tried to present a logically coherent introduction to the subject, tailored to the background of the students, as well as including a number of diversions into more sophisticated applications of these ideas. There are many statements left as exercises. I believe that those essential to the logical developments will be fairly routine. Those related to examples or diversions may be more challenging. The notes assume a basic knowledge of group theory, and metric and topological spaces. We describe some of the fundamental notions of geometric group theory, such as quasi-isometries, and aim for a basic overview of hyperbolic groups. We describe group presentations from first principles. We give an outline description of fundamental groups and covering spaces, sufficient to allow us to illustrate various results with more explicit examples. We also give a crash course on hyperbolic geometry. Again the presentation is