Alexandria Digital Research Library

A complex euclidean reflection group and its braid group

Author:
Cote, Benjamin Noel
Degree Grantor:
University of California, Santa Barbara. Mathematics
Degree Supervisor:
Jon McCammond
Place of Publication:
[Santa Barbara, Calif.]
Publisher:
University of California, Santa Barbara
Creation Date:
2016
Issued Date:
2016
Topics:
Mathematics
Genres:
Dissertations, Academic and Online resources
Dissertation:
Ph.D.--University of California, Santa Barbara, 2016
Description:

There is an interesting correspondence between groups generated by reflections, the arrangement of hyperplanes fixed by their reflections, and the braid groups arising from the complement of said hyperplanes. The spherical and euclidean Coxeter groups, their corresponding reflection arrangements and Artin groups have been previously investigated. More recent advances have been made in understanding complex spherical reflection groups and finite complex hyperplane arrangements. Little is known about the complex euclidean reflection groups, the infinite hyperplane arrangements provided by their mirrors, and their corresponding braid groups. For the affine extension of the complex reflection group Refl(G4), we construct a piecewise euclidean complex onto which the affine hyperplane complement deformation retracts, and show this is a CAT(0) space with nonregular points. Visualization techniques for the group and its geometry are described.

Physical Description:
1 online resource (112 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3b56jt8
ISBN:
9781369147124
Catalog System Number:
990046968190203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
Benjamin Coté
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