Topological complexity of subgroups of Artin's braid groups

Mark Grant, David Recio-Mitter

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review

3 Citations (Scopus)
14 Downloads (Pure)


We consider the topological complexity of subgroups of Artin's braid group consisting of braids whose associated permutations lie in some specified subgroup of the symmetric group. We give upper and lower bounds for the topological complexity of such mixed braid groups. In particular we show that the topological complexity of any subgroup of the n-strand braid group which fixes any two strands is 2n-3, extending a result of Farber and Yuzvinsky in the pure braid case. In addition, we generalise our results to the setting of higher topological complexity.
Original languageEnglish
Title of host publicationTopological complexity and related topics
EditorsMark Grant, Gregory Lupton, Lucile Vandembroucq
PublisherAmerican Mathematical Society
ISBN (Electronic)9781470444051
ISBN (Print)9781470434366
Publication statusPublished - 2018

Publication series

NameContemporary Mathematics
ISSN (Print)1098-3627
ISSN (Electronic)0271-4132

Bibliographical note

v2: 12 pages, added Section 6 on higher topological complexity


  • math.AT
  • 55M99, 55P20 (Primary), 55M30, 20J06, 68T40 (Secondary)


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