A presentation for the pure Hilden group

Stephen Tawn

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    Consider the half ball, B3 +, containing n unknotted and unlinked arcs a1, a2, . . . , an such that the boundary of each ai lies in the plane. The Hilden (or Wicket) group is the mapping class group of B3 + fixing the arcs a1 an setwise and fixing the half sphere S2 + pointwise. This group can be considered as a subgroup of the braid group on 2n strands. The pure Hilden group is defined to be the intersection of the Hilden group and the pure braid group. In a previous paper, we computed a presentation for the Hilden group using an action of the group on a cellular complex. This paper uses the same action and complex to calculate a finite presentation for the pure Hilden group. The framed braid group acts on the pure Hilden group by conjugation and this action is used to reduce the number of cases.
    Original languageEnglish
    Pages (from-to)181-202
    Number of pages22
    JournalMathematical Research Letters
    Volume20
    Issue number1
    DOIs
    Publication statusPublished - 2013

    Fingerprint

    Dive into the research topics of 'A presentation for the pure Hilden group'. Together they form a unique fingerprint.

    Cite this