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.
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Published date: October 2002
Organisations:
University of Southampton
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Local EPrints ID: 50613
URI: https://eprints.soton.ac.uk/id/eprint/50613
PURE UUID: f2093225-ca09-4291-a1f2-5bcf2b8829c2
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Date deposited: 27 Mar 2008
Last modified: 13 Jun 2019 00:39
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Author:
Paul Edward Hanham
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