On the Falk Invariant of Signed Graphic Arrangements

Weili Guo, Michele Torielli

Research output: Contribution to journalArticlepeer-review

4 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 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 languageEnglish (US)
Pages (from-to)477-488
Number of pages12
JournalGraphs and Combinatorics
Volume34
Issue number3
DOIs
StatePublished - May 1 2018
Externally publishedYes

Keywords

  • Falk invariant
  • Hyperplane arrangements
  • Lower central series
  • Sign graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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