On symplectic fillings of lens spaces

Lisca, Paolo

doi:10.1090/S0002-9947-07-04228-6

On symplectic fillings of lens spaces
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by Paolo Lisca PDF

Trans. Amer. Math. Soc. 360 (2008), 765-799 Request permission

Abstract:

Let $\overline \xi _\textrm {st}$ 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 $\xi _\textrm {st}$ on the three–sphere $S^3$. We obtain a complete classification of the symplectic fillings of $(L(p,q),\overline \xi _\textrm {st})$ 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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