On the Sigma-invariants of even Artin groups of FC-type.

In this paper we study Sigma-invariants of even Artin groups of FC-type, extending some known results for right-angled Artin groups. In particular, we define a condition that we call the strong n -link condition for a graph Γ and prove that it gives a sufficient condition for a character χ : A Γ → Z to satisfy [ χ ] ∈ Σ n (A Γ , Z). This implies that the kernel A Γ χ = ker ⁡ χ is of type FP n. We prove the homotopical version of this result as well and discuss partial results on the converse. We also provide a general formula for the free part of H n (A Γ χ ; F) as an F [ t ± 1 ] -module with the natural action induced by χ. This gives a characterization of when H n (A Γ χ ; F) is a finite dimensional vector space over F. [ABSTRACT FROM AUTHOR]