The Braid Group \(B_{4}(\mathbb S^{2})\), and the Conjugacy Classes of Its Maximal Virtually Cyclic Subgroups

  • John GuaschiEmail author
  • Daniel Juan-Pineda
  • Silvia Millán López
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


In this chapter, we focus our attention on the braid group \(B_{4}(\mathbb S^{2})\) of the sphere on four strings. The aim is to understand the structure of its maximal virtually cyclic subgroups. These results will be used in Chap. 4 to compute the lower algebraic K-theory of \(B_{4}(\mathbb S^{2})\), and to prove Theorem 1.


Braid Group Single Conjugacy Class Maximal Finite Subgroup Artin Relation Infinite Order 
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Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG, part of Springer Nature 2018

Authors and Affiliations

  • John Guaschi
    • 1
    Email author
  • Daniel Juan-Pineda
    • 2
  • Silvia Millán López
    • 3
  1. 1.Laboratoire de Mathématiques Nicolas Oresme UMR CNRS 6139Université de Caen Normandie, Normandie UniversitéCaenFrance
  2. 2.Centro de Ciencias MatemáticasUniversidad Nacional Autónoma de MéxicoMoreliaMexico
  3. 3.Colegio de Bachilleres del Estado de TlaxcalaTlaxcalaMexico

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