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Shephard Groups

Goldman, Katherine M.
http://orcid.org/0000-0002-5421-2311
http://rave.ohiolink.edu/etdc/view?acc_num=osu171329164279436

Abstract Details

2024, Doctor of Philosophy, Ohio State University, Mathematics.
We are concerned with the study of \emph{Shephard groups}, a class of groups which encompasses the Coxeter groups, Artin groups, graph products of cyclic groups, and certain complex reflection groups. We extend a well-known result that Coxeter groups are $\mathrm{CAT}(0)$ to a class of Shephard groups that have ``enough'' finite parabolic subgroups. We also show that in this setting, if the underlying Coxeter diagram is type FC, then the Shephard group is cocompactly cubulated. Our method of proof combines the works of Charney-Davis on the Deligne complex for an Artin group and of Coxeter on the classification and properties of the regular complex polytopes. Along the way we introduce a new criteria (based on work of Charney) for a simplicial complex made of simplices of shape $A_3$ to be $\mathrm{CAT}(1)$. It is our hope that this begins the study of complex reflection groups through the lens of geometric group theory, as this has quickly shown to be a fruitful approach.
Jingyin Huang (Advisor)
Jean-François Lafont (Committee Member)
Michael Davis (Committee Member)
85 p.
Mathematics
geometric group theory; nonpositive curvature; complex reflection groups

Recommended Citations

Citations

  • Goldman, K. M. (2024). Shephard Groups [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu171329164279436

    APA Style (7th edition)

  • Goldman, Katherine. Shephard Groups. 2024. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu171329164279436.

    MLA Style (8th edition)

  • Goldman, Katherine. "Shephard Groups." Doctoral dissertation, Ohio State University, 2024. http://rave.ohiolink.edu/etdc/view?acc_num=osu171329164279436

    Chicago Manual of Style (17th edition)

osu171329164279436
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© 2024, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.