Heegaard splittings and 1-relator groups

Details Heegaard splittings and 1-relator groups Heegaard splittings and 1-relator groups

2006-08-25

arxiv.org/abs/math/0608635v4

Mathematics

Geometric Topology

Paper has been withdrawn by the author due to a gap in the proof of main theorem

Scientific paper

We show that if $M$ is a fibered, orientable 3-manifold, and if $\pi_1 M$ has 1-relator presentation, then the presentation is induced by a Heegaard splitting of $M$. A corollary is that, for these manifolds, the rank of $\pi_1 M$ is equal to the "restricted" Heegaard genus of $M$. We also explore the analogy between 1-relator groups and Haken 3-manifolds, showing that every 1-relator group possesses a "1-relator hierarchy".

Affiliated with

Also associated with

No associations

Rating

Heegaard splittings and 1-relator 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 Heegaard splittings and 1-relator groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Heegaard splittings and 1-relator groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-111913