Cohomology of pure braid groups of exceptional cases.
For \((W,S)\) a finite Coxeter system realized as a reflection group in \(\mathbb{R}^n\) one defines \(Y(W)\) to be the complement to the arrangement in \(\mathbb{C}^n\). The author, [in \textit{S. Settepanella}, Topology Appl. 139, No. 1-3, 37-47 (2004; Zbl 1064.20052)], has computed the cohomology of \(Y(W)\) for the series \(A_n\), \(B_n\) and \(D_n\). The present work is a natural continuation of the latter work where the cohomology of \(A(W)\) with local coefficients \(R=\mathbb{Q}[\tau,\tau^{-1}]\) (the ring of Laurent polynomials) for the finite Coxeter groups \(H_3\), \(H_4\), \(F_4\) and \(A_n\), \(n<7\), is computed. A relevant step to obtain the results are algorithms to compute the cohomologies of the flag complex \(Fl_*(W)\).
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