Topological complexity of subgroups of Artin's braid groups

Mark Grant, David Recio-Mitter

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

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Abstract

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
Volume702
ISBN (Electronic)9781470444051
ISBN (Print)9781470434366
DOIs
Publication statusPublished - 2018

Publication series

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

Fingerprint

Topological Complexity
Artin Groups
Braid Group
Subgroup
Braid
Symmetric group
Upper and Lower Bounds
Permutation
Generalise

Keywords

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

Cite this

Grant, M., & Recio-Mitter, D. (2018). Topological complexity of subgroups of Artin's braid groups. In M. Grant, G. Lupton, & L. Vandembroucq (Eds.), Topological complexity and related topics (Vol. 702). (Contemporary Mathematics). American Mathematical Society. https://doi.org/10.1090/conm/702/14105

Topological complexity of subgroups of Artin's braid groups. / Grant, Mark; Recio-Mitter, David.

Topological complexity and related topics. ed. / Mark Grant; Gregory Lupton; Lucile Vandembroucq. Vol. 702 American Mathematical Society, 2018. (Contemporary Mathematics).

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

Grant, M & Recio-Mitter, D 2018, Topological complexity of subgroups of Artin's braid groups. in M Grant, G Lupton & L Vandembroucq (eds), Topological complexity and related topics. vol. 702, Contemporary Mathematics, American Mathematical Society. https://doi.org/10.1090/conm/702/14105
Grant M, Recio-Mitter D. Topological complexity of subgroups of Artin's braid groups. In Grant M, Lupton G, Vandembroucq L, editors, Topological complexity and related topics. Vol. 702. American Mathematical Society. 2018. (Contemporary Mathematics). https://doi.org/10.1090/conm/702/14105
Grant, Mark ; Recio-Mitter, David. / Topological complexity of subgroups of Artin's braid groups. Topological complexity and related topics. editor / Mark Grant ; Gregory Lupton ; Lucile Vandembroucq. Vol. 702 American Mathematical Society, 2018. (Contemporary Mathematics).
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