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.
|Title of host publication||Topological complexity and related topics|
|Editors||Mark Grant, Gregory Lupton, Lucile Vandembroucq|
|Publisher||American Mathematical Society|
|Publication status||Published - 2018|
- 55M99, 55P20 (Primary), 55M30, 20J06, 68T40 (Secondary)
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