We prove the Bestvina-Brady theorem, which establishes a connection between topogical properties of a flag complex $L$ and finiteness properties of a certain subgroup of the associated right-angled Artin group $G_L$. In particular, this construction provides us with examples of groups of type $F_{n}$ that are not of type $F_{n+1}$ and groups of type $FP_n$ that are not of type $FP_{n+1}$. For the proof, we employ results from the theory of non-positively curved metric spaces, where we also prove a generalized version of the Cartan-Hadamard theorem.
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