Computing the Braid Monodromy of Completely Reducible n-gonal Curves

2016/11/01 by Mehmet Emin Aktas, Aktas, Mehmet, Esra Akbaş +1
Mathematics · #14Q05 #55-04 #68W30 #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #G.4 #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1611.00249

openalex publication_date 2016/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Braid monodromy is an important tool for computing invariants of curves and surfaces. In this paper, the rectangular braid diagram (RBD) method is proposed to compute the braid monodromy of a completely reducible n-gonal curve, i.e. the curves in the form (y-y₁(x))...(y-y_n(x))=0 where n∈ ℤ⁺ and y_i∈ ℂ[x]. Also, an algorithm is presented to compute the Alexander polynomial of these curve complements using Burau representations of braid groups. Examples for each computation are provided.

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