Alexandria Digital Research Library

Braid Groups and Euclidean Simplices

Author:
Chisholm, Elizabeth Eileen Leyton
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:
2015
Issued Date:
2015
Topics:
Mathematics
Genres:
Dissertations, Academic and Online resources
Dissertation:
Ph.D.--University of California, Santa Barbara, 2015
Description:

In the early 2000s, Daan Krammer and Stephen Bigelow independently proved that braid groups are linear. They used the Lawrence-Krammer-Bigelow (LKB) representation for generic values of its variables q and t. The $t$ variable is related to the Garside structure of the braid group used in Krammer's algebraic proof. The q variable, associated with the dual Garside structure of the braid group, has received less attention.

In this dissertation we give a geometric interpretation of the q portion of the LKB representation in terms of an action of the braid group on the space of non-degenerate euclidean simplices. In our interpretation, braid group elements act by systematically reshaping (and relabeling) euclidean simplices. The reshapings associated to the simple elements in the dual Garside structure of the braid group are of an especially elementary type that we call relabeling and rescaling.

Physical Description:
1 online resource (87 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3br8qc4
ISBN:
9781339083957
Catalog System Number:
990045715480203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
Elizabeth Chisholm
File Description
Access: Public access
Chisholm_ucsb_0035D_12590.pdf pdf (Portable Document Format)