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Twisted Alexander polynomials and symplectic structures
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Friedl, Stefan and Vidussi, Stefano (2008) Twisted Alexander polynomials and symplectic structures. American Journal of Mathematics, Vol.130 (No.2). pp. 455-484. doi:10.1353/ajm.2008.0014 ISSN 0002-9327.
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Official URL: http://dx.doi.org/10.1353/ajm.2008.0014
Abstract
Let N be a closed, oriented 3-manifold. A folklore conjecture states that S1 × N admits a symplectic structure only if N admits a fibration over the circle. The purpose of this paper is to provide evidence to this conjecture studying suitable twisted Alexander polynomials of N, and showing that their behavior is the same as of those of fibered 3-manifolds. In particular, we will obtain new obstructions to the existence of symplectic structures and to the existence of symplectic forms representing certain cohomology classes of S1 × N. As an application of these results we will show that S1 × N(P) does not admit a symplectic structure, where N(P) is the 0-surgery along the pretzel knot P = (5, -3, 5), answering a question of Peter Kronheimer.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | American Journal of Mathematics | ||||
Publisher: | The Johns Hopkins University Press | ||||
ISSN: | 0002-9327 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.130 | ||||
Number: | No.2 | ||||
Page Range: | pp. 455-484 | ||||
DOI: | 10.1353/ajm.2008.0014 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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