A polynomial invariant for plane curve complements: Krammer polynomials. (English) Zbl 1423.14207
Summary: We use the Krammer representation of the braid group in Libgober’s invariant and construct a new multivariate polynomial invariant for curve complements: Krammer polynomial. We show that the Krammer polynomial of an essential braid is equal to zero. We also compute the Krammer polynomials of some certain \(n\)-gonal curves.
MSC:
| 14H50 | Plane and space curves |
| 14H20 | Singularities of curves, local rings |
| 14H30 | Coverings of curves, fundamental group |
| 20F36 | Braid groups; Artin groups |
| 14H45 | Special algebraic curves and curves of low genus |
Software:
SageMathReferences:
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