1. On the Falk Invariant of Shi and Linial Arrangements.
- Author
-
Guo, Weili and Torielli, Michele
- Subjects
- *
OPEN-ended questions , *CONES , *FUNDAMENTAL groups (Mathematics) - 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 representations of certain gain graphs. As a corollary, we compute the Falk invariant for the cone of the braid, Shi, Linial, and semiorder arrangements. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF