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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On symplectic fillings of lens spaces


Author: Paolo Lisca
Journal: Trans. Amer. Math. Soc. 360 (2008), 765-799
MSC (2000): Primary 57R17; Secondary 53D35
Published electronically: September 18, 2007
MathSciNet review: 2346471
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Abstract: Let $ \overline\xi_{\rm st}$ be the contact structure naturally induced on the lens space $ L(p,q)=S^3/\mathbb{Z}/p\mathbb{Z}$ by the standard contact structure $ \xi_{\rm st}$ on the three-sphere $ S^3$. We obtain a complete classification of the symplectic fillings of $ (L(p,q),\overline\xi_{\rm st})$ up to orientation-preserving diffeomorphisms. In view of our results, we formulate a conjecture on the diffeomorphism types of the smoothings of complex two-dimensional cyclic quotient singularities.


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Additional Information

Paolo Lisca
Affiliation: Dipartimento di Matematica “L. Tonelli”, Università di Pisa, I-56127 Pisa, Italy
Email: lisca@dm.unipi.it

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04228-6
PII: S 0002-9947(07)04228-6
Received by editor(s): October 11, 2005
Published electronically: September 18, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.