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thesis.pdf (304.88 KB)
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THE DEFORMATION THEORY OF DISCRETE REFLECTION GROUPS AND PROJECTIVE STRUCTURES
Author Info
Greene, Ryan M
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1374156914
Abstract Details
Year and Degree
2013, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
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.
Committee
Michael Davis (Advisor)
Lafont Jean-Francois (Committee Member)
Crichton Ogle (Committee Member)
Larry Brown (Committee Member)
Pages
50 p.
Subject Headings
Mathematics
Keywords
reflection groups, Coxeter groups, reflection orbifolds, Coxeter orbifolds, convex real projective structures, deformation theory, group cohomology, Davis complex
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Citations
Greene, R. M. (2013).
THE DEFORMATION THEORY OF DISCRETE REFLECTION GROUPS AND PROJECTIVE STRUCTURES
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1374156914
APA Style (7th edition)
Greene, Ryan.
THE DEFORMATION THEORY OF DISCRETE REFLECTION GROUPS AND PROJECTIVE STRUCTURES.
2013. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1374156914.
MLA Style (8th edition)
Greene, Ryan. "THE DEFORMATION THEORY OF DISCRETE REFLECTION GROUPS AND PROJECTIVE STRUCTURES." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1374156914
Chicago Manual of Style (17th edition)
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Document number:
osu1374156914
Download Count:
411
Copyright Info
© 2013, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.