A polynomial invariant for plane curve complements: Krammer polynomials
نویسندگان
چکیده
منابع مشابه
A Polynomial Invariant for Plane Curve Complements: Krammer Polynomials
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.
متن کاملInvariant Subspaces of the Lawrence–krammer Representation
The Lawrence–Krammer representation was used in 2000 to show the linearity of the braid group. The problem had remained open for many years. The fact that the Lawrence–Krammer representation of the braid group is reducible for some complex values of its two parameters is now known, as well as the complete description of these values. It is also known that when the representation is reducible, t...
متن کاملTwisted Alexander Polynomial for the Lawrence-krammer Representation
In this paper, we prove that the twisted Alexander polynomial for the Lawrence-Krammer representation of the braid group B4 is trivial. This gives an answer for the problem whether the twisted Alexander polynomial for given faithful representations is always non-trivial.
متن کاملThe Orevkov Invariant of an Affine Plane Curve
We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the Orevkov invariant.
متن کاملAlgebraic invariant curves of plane polynomial differential systems
We consider a plane polynomial vector field P(x, y) dx +Q(x, y) dy of degree m > 1. With each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential ω = dx/P = dy/Q. The asymptotic estimate of the degree of an arbitrary algebraic invariant curve is found. In the smooth case this estimate has already been found by Cerveau and Lins Neto ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Singularities
سال: 2018
ISSN: 1949-2006
DOI: 10.5427/jsing.2018.17c