Torsion-freeness conjecture for the cohomology of affine Weyl toric arrangement complements

About 16 years old · traced to

Let W~\widetilde{W} be an affine Weyl group, and let TW~\mathcal{T}_{\widetilde{W}} be the corresponding toric arrangement. Its complement is the space obtained by removing the arrangement from the associated torus. Torsion-freeness conjecture. The integer cohomology of this complement is torsion free; consequently, it coincides with the De Rham cohomology computed by De Concini and Procesi. The conjecture is stated as a generalization of the explicit computation for the B2B_2 toric arrangement, where the homology and cohomology are torsion free. Although the source says it will be proved in a future paper, the supplied status marks it as resolved.

References

Primary source

Luca Moci and Simona Settepanella, “The homotopy type of toric arrangements”, arXiv:1009.3622 (2010).

Additional references

2 papers in this index state this conjecture (2010). The statement above is taken from the most recent of them; the others are arXiv:1008.0631.

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.