Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence
Abstract
We study the crossing matrix of a braid and introduce a polynomial invariant for braid systems that is invariant under Hurwitz equivalence. As an application to the study of surface braids and surface links, we also define an invariant that can be used as an indicator of the necessity of Euler fusion or fission between braid systems.
Fields of Study & Subjects
Geometric and Algebraic Topology
Algebraic Geometry and Number Theory
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 5 January 2026
- Document type
- Preprint