TY - JOUR
TI - Coarse geometry of Out(A_{1} * ... * A_{n})
DO - https://doi.org/doi:10.7282/t3-jwy0-bd33
PY - 2019
AB - In this thesis we have examined ?n := Out(Gn) from the perspective of geometric group theory, where Gn = A1 ? ... ? An, is a finite free product and each Ai is a finite group. We wanted to inspect hyperbolicity and relative hyperbolicity of such groups. We used the Out(Gn) action on the Guirardel-Levitt deformation space to find a virtual generating set and prove quasi isometric embedding of a large class of subgroups. To prove non-distortion we used arguments similar to those used by Handel-Mosher and Alibegovi?. We used these subgroups to prove that ?n is thick in higher complexities. Behrstock-Dru?u-Mosher showed that thickness implies that the groups are non relatively hyperbolic for higher complexities.
KW - Geometric group theory
KW - Mathematical Sciences
LA - English
ER -