Regular Cocycles and Biautomatic Structures

Details Regular Cocycles and Biautomatic Structures Regular Cocycles and Biautomatic Structures

1994-11-07

arxiv.org/abs/math/9411203v1

Mathematics

Group Theory

Plain Tex, 11 pages, no figures

Scientific paper

Let $E$ be a virtually central extension of the group $G$ by a finitely generated abelian group $A$. We show that $E$ carries a biautomatic structure if and only if $G$ has a biautomatic structure $L$ for which the cohomology class of the extension is represented by an $L$-regular cocycle. Moreover, a cohomology class is $L$-regular if some multiple of it is or if its restriction to some finite index subgroup is. We also show that the entire second cohomology of a Fuchsian group is regular, so any virtually central extension is biautomatic. In particular, if the fundamental group of a Seifert fibered 3-manifold is not virtually nilpotent then it is biautomatic. ECHLPT had shown automaticity in this case and in an unpublished 1992 preprint Gersten constructed a biautomatic structure for circle bundles over hyperbolic surfaces and asked if the same could be done for these Seifert fibered 3-manifolds.

Affiliated with

Also associated with

No associations

Rating

Regular Cocycles and Biautomatic Structures 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 Regular Cocycles and Biautomatic Structures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regular Cocycles and Biautomatic Structures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-360627