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ISSN 1088-6850(e) ISSN 0002-9947(p)

On symplectic fillings of lens spaces

Author(s): Paolo Lisca
Journal: Trans. Amer. Math. Soc. 360 (2008), 765-799.
MSC (2000): Primary 57R17; Secondary 53D35
Posted: 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 . 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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