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THE DEFORMATION THEORY OF DISCRETE REFLECTION GROUPS AND PROJECTIVE STRUCTURES
Greene, Ryan M

2013, Doctor of Philosophy, Ohio State University, Mathematics.
We study deformations of discrete groups generated by linear re
ections and associated
geometric structures on orbifolds via cohomology of Coxeter groups with
coecients in the adjoint representation associated to a discrete representation.
We completely describe a cochain complex that computes this cohomology for an
arbitrary discrete re
ection group and, as a consequence of this description, give
a vanishing theorem for cohomology in dimensions greater than 2. As an application,
we discuss some situations in which the cohomology vanishes in dimension 2
as well. In particular, we are able to give a proof of a recent result of Choi and
Lee on deforming a certain class of hyperbolic orbifolds through non-hyperbolic
projective structures in cohomological language and give some insight into
how the result can be extended.
Michael Davis (Advisor)
Lafont Jean-Francois (Committee Member)
Crichton Ogle (Committee Member)
Larry Brown (Committee Member)
50 p.

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Greene, R. (2013). THE DEFORMATION THEORY OF DISCRETE REFLECTION GROUPS AND PROJECTIVE STRUCTURES. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Greene, Ryan. "THE DEFORMATION THEORY OF DISCRETE REFLECTION GROUPS AND PROJECTIVE STRUCTURES." Electronic Thesis or Dissertation. Ohio State University, 2013. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Greene, Ryan "THE DEFORMATION THEORY OF DISCRETE REFLECTION GROUPS AND PROJECTIVE STRUCTURES." Electronic Thesis or Dissertation. Ohio State University, 2013. https://etd.ohiolink.edu/

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