- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Braid groups, orderings, and algorithms
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
Braid groups, orderings, and algorithms Kim, Djun Maximillian
Abstract
We define a natural and readily calculated bi-invariant strict total ordering of the n-strand pure braid group Pn. It is defined algebraically, using the Artin decomposition of Pn as a semi-direct product of free groups, together with a specific ordering of free groups using the Magnus expansion. This definition extends to define bi-orderings of more general semi-direct products involving free groups, including the fundamental groups of the complements of fibretype hyperplane arrangements. After basic properties of this "Artin-Magnus" ordering are established, we compare it to existing orderings on Pn, including the restriction of the Dehornoy ordering to Pn. Finally, we present algorithms to compute the Dehornoy ordering on the full braid group Bn, and the Artin-Magnus ordering on Pn. An implementation of these algorithms is included as part of a library of objects for symbolic computation with braids.
Item Metadata
Title |
Braid groups, orderings, and algorithms
|
Creator | |
Publisher |
University of British Columbia
|
Date Issued |
1999
|
Description |
We define a natural and readily calculated bi-invariant strict total ordering of
the n-strand pure braid group Pn. It is defined algebraically, using the Artin
decomposition of Pn as a semi-direct product of free groups, together with a
specific ordering of free groups using the Magnus expansion. This definition
extends to define bi-orderings of more general semi-direct products involving
free groups, including the fundamental groups of the complements of fibretype
hyperplane arrangements.
After basic properties of this "Artin-Magnus" ordering are established,
we compare it to existing orderings on Pn, including the restriction of the
Dehornoy ordering to Pn.
Finally, we present algorithms to compute the Dehornoy ordering on the
full braid group Bn, and the Artin-Magnus ordering on Pn. An implementation
of these algorithms is included as part of a library of objects for symbolic
computation with braids.
|
Extent |
3911660 bytes
|
Genre | |
Type | |
File Format |
application/pdf
|
Language |
eng
|
Date Available |
2009-06-30
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
|
DOI |
10.14288/1.0079908
|
URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
|
Graduation Date |
1999-05
|
Campus | |
Scholarly Level |
Graduate
|
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.