Orbit Braid Action on a Finite Generated Group

2019/12/11 by Haochen Qiu, Qiu, Haochen
Mathematics · #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1912.05450

openalex publication_date 2019/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper aims to generalize Artin's ideas to establish an one-to-one correspondence between the orbit braid group B^orb_n(ℂ,ℤ_p) and a quotient of a group formed by some particular homeomorphisms of a punctured plane. First, we find a faithful representation of B^orb_n(ℂ,ℤ_p) in a finite generated group whose generators are corresponding to generators of fundamental group of the punctured plane, by examining the representation from B^orb_n(ℂ^×,ℤ_p) to the fundamental group is faithful. Then we investigate some characterizations of orbit braid representation to come to our conclusion.

Citations

• A theory of orbit braids

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