@inbook{98ddb5ec54674c3c85349029d1d6092f,

title = "Topological complexity of subgroups of Artin's braid groups",

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.",

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

author = "Mark Grant and David Recio-Mitter",

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

year = "2018",

doi = "10.1090/conm/702/14105",

language = "English",

isbn = "9781470434366",

volume = "702",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

editor = "Mark Grant and Lupton, {Gregory } and Vandembroucq, {Lucile }",

booktitle = "Topological complexity and related topics",

address = "United States",

}