Symplectic S^1 x N^3, subgroup separability, and vanishing Thurston norm

Details Symplectic S^1 x N^3, subgroup separability, and vanishing Thurston norm Symplectic S^1 x N^3, subgroup separability, and vanishing Thurston norm

2007-01-24

arxiv.org/abs/math/0701717v2

Mathematics

Geometric Topology

16 pages. Minor revision of Version 1. To appear in J. Amer. Math. Soc

Scientific paper

Let N be a closed, oriented 3-manifold. A folklore conjecture states that $S^{1} \times N$ admits a symplectic structure if and only if $N$ admits a fibration over the circle. We will prove this conjecture in the case when N is irreducible and its fundamental group satisfies appropriate subgroup separability conditions. This statement includes 3-manifolds with vanishing Thurston norm, graph manifolds and 3-manifolds with surface subgroup separability (a condition satisfied conjecturally by all hyperbolic 3-manifolds). Our result covers, in particular, the case of 0-framed surgeries along knots of genus one. The statement follows from the proof that twisted Alexander polynomials decide fiberability for all the 3-manifolds listed above. As a corollary, it follows that twisted Alexander polynomials decide if a knot of genus one is fibered.

Affiliated with

Also associated with

No associations

Rating

Symplectic S^1 x N^3, subgroup separability, and vanishing Thurston norm 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 Symplectic S^1 x N^3, subgroup separability, and vanishing Thurston norm, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symplectic S^1 x N^3, subgroup separability, and vanishing Thurston norm will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-329074