Mathematics – Geometric Topology
Scientific paper
2011-10-30
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.
Gonçalves Daciberg Lima
Guaschi John
No associations
LandOfFree
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.
Profile ID: LFWR-SCP-O-12851