### Abstract

Original language | English |
---|---|

Title of host publication | Topological complexity and related topics |

Editors | Mark Grant, Gregory Lupton, Lucile Vandembroucq |

Publisher | American Mathematical Society |

Volume | 702 |

ISBN (Electronic) | 9781470444051 |

ISBN (Print) | 9781470434366 |

DOIs | |

Publication status | Published - 2018 |

### Publication series

Name | Contemporary Mathematics |
---|---|

Publisher | AMS |

ISSN (Print) | 1098-3627 |

ISSN (Electronic) | 0271-4132 |

### Fingerprint

### Keywords

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

### Cite this

*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.

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

*Topological complexity and related topics.*vol. 702, Contemporary Mathematics, American Mathematical Society. https://doi.org/10.1090/conm/702/14105

}

TY - CHAP

T1 - Topological complexity of subgroups of Artin's braid groups

AU - Grant, Mark

AU - Recio-Mitter, David

N1 - v2: 12 pages, added Section 6 on higher topological complexity

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - math.AT

KW - 55M99, 55P20 (Primary), 55M30, 20J06, 68T40 (Secondary)

U2 - 10.1090/conm/702/14105

DO - 10.1090/conm/702/14105

M3 - Chapter (peer-reviewed)

SN - 9781470434366

VL - 702

T3 - Contemporary Mathematics

BT - Topological complexity and related topics

A2 - Grant, Mark

A2 - Lupton, Gregory

A2 - Vandembroucq, Lucile

PB - American Mathematical Society

ER -