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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
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Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

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.

Keywords

Braid Group Single Conjugacy Class Maximal Finite Subgroup Artin Relation Infinite Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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