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The CAT(0) dimension of 3-generator Artin groups

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
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

Identifiers

Local EPrints ID: 50613
URI: https://eprints.soton.ac.uk/id/eprint/50613
PURE UUID: f2093225-ca09-4291-a1f2-5bcf2b8829c2
ORCID for Graham Niblo: ORCID iD orcid.org/0000-0003-0648-7027

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Date deposited: 27 Mar 2008
Last modified: 13 Jun 2019 00:39

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