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arXiv:math/0608635 [math.GT]AbstractReferencesReviewsResources

Heegaard splittings and 1-relator groups

Joseph D. Masters

Published 2006-08-25, updated 2012-04-21Version 4

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".

Comments: Paper has been withdrawn by the author due to a gap in the proof of main theorem
Categories: math.GT, math.GR
Subjects: 57M05, 57M07
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