On symplectic fillings of lens spaces
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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.References
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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
- Received by editor(s): October 11, 2005
- Published electronically: September 18, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 765-799
- MSC (2000): Primary 57R17; Secondary 53D35
- DOI: https://doi.org/10.1090/S0002-9947-07-04228-6
- MathSciNet review: 2346471