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 Falk invariant of the arrangement since Falk gave the first formula and asked to give a combinatorial interpretation. In this article, we give a combinatorial formula for the Falk invariant of a signed graphic arrangement that do not have a B2 as sub-arrangement.
Original language | English (US) |
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Pages (from-to) | 477-488 |
Number of pages | 12 |
Journal | Graphs and Combinatorics |
Volume | 34 |
Issue number | 3 |
DOIs | |
State | Published - May 1 2018 |
Externally published | Yes |
Keywords
- Falk invariant
- Hyperplane arrangements
- Lower central series
- Sign graph
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics