# Morse theory and finiteness properties of groups

@article{Bestvina1997MorseTA,
title={Morse theory and finiteness properties of groups},
journal={Inventiones mathematicae},
year={1997},
volume={129},
pages={445-470}
}
• Published 1 August 1997
• Mathematics
• Inventiones mathematicae
Abstract. We examine the finiteness properties of certain subgroups of “right angled” Artin groups. In particular, we find an example of a group that is of type FP(Z) but is not finitely presented.
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## References

SHOWING 1-10 OF 10 REFERENCES
The Bieri–Neumann–Strebel Invariants for Graph Groups
• Mathematics
• 1993
Given a finite simplicial graph ${\cal G}$, the graph group $G{\cal G}$" is the group with generators in one-to-one correspondence with the vertices of ${\cal G}$ and with relations stating two
Cohomologie des groupes discrets
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