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arXiv · 2101.04517

On the Falk invariant of Shi and Linial arrangements

Weili Guo·Michele Torielli
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Abstract

It is an open question to give a combinatorial interpretation of the Falk invariant of a hyperplane arrangement, i.e. the third rank of successive quotients in the lower central series of the fundamental group of the arrangement. In this article, we give a combinatorial formula for this invariant in the case of hyperplane arrangements that are complete lift representation of certain gain graphs. As a corollary, we compute the Falk invariant for the cone of the braid, Shi, Linial and semiorder arrangements.

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Weili Guo, Michele Torielli. 2021-01-10. On the Falk invariant of Shi and Linial arrangements. https://doi.org/10.1007/s00454-020-00266-0

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