A Look at Right-Angled Artin Groups.
November 05, 2004 02:00 PM to 03:00 PM
Speakers:
Suciu, Alexandru
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Abstract: |
A finite simplicial graph $\Gama$ determines in a natural way two groups:
the right-angled Artin group $G_{\Gama}$, with one generator for each
vertex $v$, and with one commutator relation $vw=wv$ for each pair of
vertices joined by an edge; and the Bestvina-Brady group $N_{\Gama}$,
obtained as the kernel of the projection from $G_{\Gama}$ to $\mathbb{Z}$,
which sends each generator $v$ to 1. As is well-known, many of the
properties of these two groups are determined by the topology of the flag
complex of $\Gama$. In this spirit, we explain in this talk how to compute
the lower central series quotients, the Chern quotients, and the (first)
resonance variety of the groups $G_{\Gama}$ and $N_{\Gama}$, directly from
the graph. |
Keywords: |
Hyperplane arrangements; cubical complex; exterior Stanley-Riesner ring; L.C.S. formula; holonomy Lie algebra. |
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