Outer automorphisms of finitely generated free groups

Date

2023-12

Author

Olguner, Egehan

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In this thesis, we will examine the outer automorphism group of free groups with n generators (Out(Fn)) by defining the Outer space (or Culler-Vogtmann space) whose points are homotopy classes of graphs with one vertex, on which Out(Fn) has a natural group action. We will further define the (rational) Euler characteristic for discrete groups, and use the Outer space to calculate the Euler characteristic of Out(Fn). Lastly, we will examine the finite subgroups of Out(Fn) and use the gathered results to calculate for a prime number p, the exponent of p in the denominator of the Euler characteristic of Out(Fn).

Subject Keywords

Outer automorphism group of a free group, Outer space, Euler characteristic of a discrete group

URI

https://hdl.handle.net/11511/108199

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Graduate School of Natural and Applied Sciences, Thesis