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Research Statement Robert Sulway Autumn 2009 My primary research area is geometric group theory, with a secondary interest
 

Summary: Research Statement Robert Sulway Autumn 2009
My primary research area is geometric group theory, with a secondary interest
in low-dimensional Topology. And, as a geometric group theorist, I attempt to under-
stand groups by understanding the geometry of the spaces on which the groups act. In
particular, I am seeking to understand the class of groups known as affine-type Artin
groups, by constructing the groups according to a procedure that also provides a space
on which the groups act. This relatively new procedure is called the `pulling-apart'
process, and it constructs braided versions of previously known groups. For example,
applying the process to a symmetric group yields the corresponding braid group. In
my dissertation I apply this process to alternating groups, crystallographic groups
(particularly the 17 wallpaper groups) and 3-dimensional affine Coxeter groups, com-
piling detailed structural information about the resulting groups and spaces. In Sec-
tion 1 I describe the process of pulling groups apart and in Section 2 I outline my
own contributions.
1 Coxeter Groups and Artin Groups
A Coxeter group is any group with presentation of the form
r1, . . . , rn | (rirj)mij
= 1 ,
where mij N {}, mii = 1 and mij = mji for all i and j and when mij = this
indicates that the presentation lacks a relation involving ri and rj. Instead of using

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics