### University of Arkansas Topology Seminar: 2/13/2014

### Speaker: Matt Day

### Title: Splittings of right-angled Artin groups over links, and
applications

Abstract: I will discuss work in progress, joint
with Henry Wilton, on right-angled Artin groups (raags). We formulate
a definition of the "algebraic link" of an element of a raag; this
generalizes the relationship between a standard generator of a raag
and the subgroup generated by its link in the defining graph. We
study HNN splittings of raags where the edge group is the algebraic
link of the stable letter (this is a certain kind of action on a
tree). Our main result is that every such splitting is the image of
an "obvious" one under an automorphism. We also develop a new
inductive scheme for studying automorphism groups of raags, and apply
the main result to reprove some classic results about raags, including
Laurence's theorem (which gives generators for the automorphism group
of a raag).

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