The classification of the virtually cyclic subgroups of the sphere braid groups

Details The classification of the virtually cyclic subgroups of the sphere braid groups The classification of the virtually cyclic subgroups of the sphere braid groups

2011-10-30

arxiv.org/abs/1110.6628v1

Mathematics

Geometric Topology

96 pages, 11 figures

Scientific paper

We study the problem of determining the isomorphism classes of the virtually cyclic subgroups of the n-string braid groups B_n(S^2) of the 2-sphere S^2. If n is odd, or if n is even and sufficiently large, we obtain the complete classification. For small even values of n, the classification is complete up to an explicit finite number of open cases. In order to prove our main theorem, we obtain a number of other results of independent interest, notably the characterisation of the centralisers and normalisers of the finite cyclic and dicyclic subgroups of B_n(S^2), a result concerning conjugate powers of finite order elements, an analysis of the isomorphism classes of the amalgamated products that occur as subgroups of B_n(S^2), as well as an alternative proof of the fact that the universal covering space of the n-th configuration space of S^2 has the homotopy type of S^3 if n is greater than or equal to three.

Affiliated with

Also associated with

No associations

Rating

The classification of the virtually cyclic subgroups of the sphere braid groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The classification of the virtually cyclic subgroups of the sphere braid groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The classification of the virtually cyclic subgroups of the sphere braid groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-12851