The CAT(0) dimension of 3-generator Artin groups
The CAT(0) dimension of 3-generator Artin groups
The three generator Artin groups A(m,n.2) are known to be have CAT(O) dimension strictly greater than two if both m and n are odd [BC]. In Chapter 1 we introduce the notions of CAT(O) dimension and three generator Artin
groups.
In Chapter 2 we show that if one of m or n is even, then the three generator Artin group has CAT(O) dimension two.
In Chapter 3 we extend work by Noel Brady and John Crisp [BC] to enlarge the subclass of groups A(m.n.2) known to have CAT(O) dimension three.
In Chapter 4 we classify the structure of a canonical cell complex which the group A(m,n,2) acts on for the case where m is even, greater or equal to six and not divisible by four and n is prime, greater or equal to five.
Finally, in Chapter 5 we use the results of Chapter 4 to exhibit classes of rank four Artin groups with CAT(O) dimension two. and a class of rank six Artin groups with CAT(O) dimension two.
Hanham, Paul Edward
b7624343-10ab-4c6c-b7ae-cb242c877593
October 2002
Hanham, Paul Edward
b7624343-10ab-4c6c-b7ae-cb242c877593
Niblo, Graham
43fe9561-c483-4cdf-bee5-0de388b78944
Hanham, Paul Edward
(2002)
The CAT(0) dimension of 3-generator Artin groups.
University of Southampton, Faculty of Mathematics, Doctoral Thesis, 169pp.
Record type:
Thesis
(Doctoral)
Abstract
The three generator Artin groups A(m,n.2) are known to be have CAT(O) dimension strictly greater than two if both m and n are odd [BC]. In Chapter 1 we introduce the notions of CAT(O) dimension and three generator Artin
groups.
In Chapter 2 we show that if one of m or n is even, then the three generator Artin group has CAT(O) dimension two.
In Chapter 3 we extend work by Noel Brady and John Crisp [BC] to enlarge the subclass of groups A(m.n.2) known to have CAT(O) dimension three.
In Chapter 4 we classify the structure of a canonical cell complex which the group A(m,n,2) acts on for the case where m is even, greater or equal to six and not divisible by four and n is prime, greater or equal to five.
Finally, in Chapter 5 we use the results of Chapter 4 to exhibit classes of rank four Artin groups with CAT(O) dimension two. and a class of rank six Artin groups with CAT(O) dimension two.
Text
00247959.pdf
- Other
More information
Published date: October 2002
Organisations:
University of Southampton
Identifiers
Local EPrints ID: 50613
URI: http://eprints.soton.ac.uk/id/eprint/50613
PURE UUID: f2093225-ca09-4291-a1f2-5bcf2b8829c2
Catalogue record
Date deposited: 27 Mar 2008
Last modified: 13 Jun 2019 00:39
Export record
Contributors
Author:
Paul Edward Hanham
University divisions
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
