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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Symplectic tori in homotopy $\mathbf{E}(1)$'s


Author: Stefano Vidussi
Journal: Proc. Amer. Math. Soc. 133 (2005), 2477-2481
MSC (2000): Primary 57R17, 57R57
Published electronically: March 14, 2005
MathSciNet review: 2138891
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Abstract: This short note presents a simple construction of nonisotopic symplectic tori representing the same primitive homology class in the symplectic $4$-manifold $E(1)_{K}$, obtained by knot surgery on the rational elliptic surface $E(1) = \mathbb{P} ^{2} \char93 9 {\overline{\mathbb{P} }^{2}}$ with the left-handed trefoil knot $K$. $E(1)_{K}$ has the simplest homotopy type among simply-connected symplectic $4$-manifolds known to exhibit such a property.


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Additional Information

Stefano Vidussi
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 70803
Email: vidussi@math.ksu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07527-1
PII: S 0002-9939(05)07527-1
Keywords: Symplectic $4$-manifolds, Seiberg-Witten theory
Received by editor(s): July 1, 2003
Received by editor(s) in revised form: September 8, 2003
Published electronically: March 14, 2005
Additional Notes: The author was supported in part by NSF Grant DMS-0306074.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2005 American Mathematical Society