Blocked-braid Groups

2013/07/20 by D. Maglia, N. Sabadini, Maglia, D. +3
Mathematics · #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.CT

paper · pdf · doi:10.48550/arxiv.1307.5383

arxiv created 2013/07/20 · openalex publication_date 2013/07/20 · arxiv updated 2013/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce and study a family of groups BB_n, called the blocked-braid groups, which are quotients of Artin's braid groups B_n, and have the corresponding symmetric groups Σ_n as quotients. They are defined by adding a certain class of geometrical modifications to braids. They arise in the study of commutative Frobenius algebras and tangle algebras in braided strict monoidal categories. A fundamental equation true in BB_n is Dirac's Belt Trick; that torsion through 4π is equal to the identity. We show that BB_n is finite for n=1,2 and 3 but infinite for n>3.

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