2001/10/10 by Mina Teicher, M. Teicher, Teicher, M. +2
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #math.GR
paper · pdf · doi:10.48550/arxiv.math/0110110
arxiv created 2001/10/10 · openalex publication_date 2001/10/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the problem of Hurwitz equivalence of Δ2 factorization in the braid group, we address the problem of Hurwitz equivalence in the symmetric group, obtained by projecting the Δ2 factorizations into Sn. We get 1Sn factorizations with transposition factors. Looking at the transpositions as the edges in a graph, we show that two factorizations are Hurwitz equivalent if and only if their graphs have the same weighted connected components. The main result of this paper will help us to compute the "Braid Monodromy Type" invariant. The graph structure gives a weaker but very easy to compute invariant to distinguish between diffeomorphic surfaces which are not deformation of each other.