The Library
Symplectic $\mathbf{S}^{1} \times N^3$, subgroup separability, and vanishing Thurston norm
Tools
Friedl, Stefan and Vidussi, Stefano (2007) Symplectic $\mathbf{S}^{1} \times N^3$, subgroup separability, and vanishing Thurston norm. Journal of the American Mathematical Society, Vol.21 (No.2). pp. 597-611. doi:10.1090/S0894-0347-07-00577-2 ISSN 1088-6834.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1090/S0894-0347-07-00577-2
Abstract
Let be a closed, oriented -manifold. A folklore conjecture states that admits a symplectic structure if and only if admits a fibration over the circle. We will prove this conjecture in the case when is irreducible and its fundamental group satisfies appropriate subgroup separability conditions. This statement includes -manifolds with vanishing Thurston norm, graph manifolds and -manifolds with surface subgroup separability (a condition satisfied conjecturally by all hyperbolic -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 -manifolds listed above. As a corollary, it follows that twisted Alexander polynomials decide if a knot of genus one is fibered.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of the American Mathematical Society | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 1088-6834 | ||||
Official Date: | 2007 | ||||
Dates: |
|
||||
Volume: | Vol.21 | ||||
Number: | No.2 | ||||
Page Range: | pp. 597-611 | ||||
DOI: | 10.1090/S0894-0347-07-00577-2 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |