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 language | English (US) |
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Pages (from-to) | 301-317 |
Number of pages | 17 |
Journal | Australasian Journal of Combinatorics |
Volume | 77 |
State | Published - 2020 |
Externally published | Yes |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics