Mathematics – Geometric Topology
Scientific paper
2001-09-22
Mathematics
Geometric Topology
Scientific paper
The equivalence (or weak equivalence) classes of orientation-preserving free actions of a finite group G on an orientable 3-dimensional handlebody of genus g can be enumerated in terms of sets of generators of G. They correspond to the equivalence classes of generating n-vectors of elements of G, where n=1+(g-1)/|G|, under Nielsen equivalence (or weak Nielsen equivalence). For abelian and dihedral G, this allows a complete determination of the equivalence and weak equivalence classes of actions for all genera. Additional information is obtained for solvable groups and for the groups PSL(2,3^p) with p prime. For all G, there is only one equivalence class of actions on the genus g handlebody if g is at least 1+r(G)|G|, where r(G) is the maximal length of a chain of subgroups of G. There is a stabilization process that sends an equivalence class of actions to an equivalence class of actions on a higher genus, and some results about its effects are obtained.
McCullough Darryl
Wanderley Marcus
No associations
LandOfFree
Free actions on handlebodies 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 Free actions on handlebodies, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Free actions on handlebodies will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-565163