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On the quasi-isometric rigidity of a class of right-angled Coxeter groups

Bounds, Jordan
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1561561078356503

Abstract Details

2019, Doctor of Philosophy (Ph.D.), Bowling Green State University, Mathematics/Mathematics (Pure).
To each finite simplicial graph Γ there is an associated right-angled Coxeter group given by the presentation WΓ=⟨ v ∈ V(Γ)| v2=1 for all v ∈ V(Γ); v1v2=v2v1 if and only if (v1, v2) ∈ E(Γ)⟩, where V(Γ),E(Γ) denote the vertex set and edge set of Γ respectively. In this dissertation, we discuss the quasi-isometric rigidity of the class of right-angled Coxeter groups whose defining graphs are given by generalized polygons. We begin with a review of some helpful preliminary concepts, including a discussion on the current state of the art of the quasi-isometric classification of right-angled Coxeter groups. We then prove in detail that for any given joins of finite generalized thick m-gons Γ1,Γ2 with m ∈ {3,4,6,8}, the corresponding right-angled Coxeter groups are quasi-isometric if and only if Γ1 and Γ2 are isomorphic.
Xiangdong Xie, Ph.D. (Advisor)
Maria Bidart, Ph.D. (Other)
Kit Chan, Ph.D. (Committee Member)
Mihai Staic, Ph.D. (Committee Member)
65 p.
Mathematics
geometric group theory; right-angled Coxeter groups; group theory; abstract algebra; quasi-isometric classification

Recommended Citations

Citations

  • Bounds, J. (2019). On the quasi-isometric rigidity of a class of right-angled Coxeter groups [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1561561078356503

    APA Style (7th edition)

  • Bounds, Jordan. On the quasi-isometric rigidity of a class of right-angled Coxeter groups. 2019. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1561561078356503.

    MLA Style (8th edition)

  • Bounds, Jordan. "On the quasi-isometric rigidity of a class of right-angled Coxeter groups." Doctoral dissertation, Bowling Green State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1561561078356503

    Chicago Manual of Style (17th edition)

bgsu1561561078356503
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© 2019, all rights reserved.
This open access ETD is published by Bowling Green State University and OhioLINK.