On Symplectic Caps

Chapter
Part of the Progress in Mathematics book series (PM, volume 296)

Abstract

An important class of contact 3-manifolds comprises those that arise as links of rational surface singularities with reduced fundamental cycle. We explicitly describe symplectic caps (concave fillings) of such contact 3-manifolds. As an application, we present a new obstruction for such singularities to admit rational homology disk smoothings.

Keywords

Three-manifold Symplectic cap Handle attachment Link Open book 

Notes

Acknowledgments

The authors would like to acknowledge support from the Hungarian–South African Bilateral Project NRF 62124 (ZA-15/2006), and we thank András Némethi for many useful conversations. The second author was also supported by OTKA T67928. The authors would also like to thank Chris Wendl for pointing out an important mistake in the first version of this paper.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA
  2. 2.Rényi Institute of MathematicsBudapestHungary

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