On the falk invariant of hyperplane arrangements attached to gain graphs

Weili Guo, Michele Torielli

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The fundamental group of the complement of a hyperplane arrangement in a complex vector space is an important topological invariant. The third rank of successive quotients in the lower central series of the fundamental group was called the Falk invariant of the arrangement since Falk gave the first formula and asked for a combinatorial interpretation. In this article, we give a combinatorial formula for the Falk invariant of hyperplane arrangements attached to certain gain graphs.

Original languageEnglish (US)
Pages (from-to)301-317
Number of pages17
JournalAustralasian Journal of Combinatorics
Volume77
StatePublished - 2020
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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