Symplectic constructions on 4-manifolds
Dissertation, University of Texas (December 1996), 1-92.

In this paper we give various conditions under which a rational blowdown can be done symplectically. This result may be used to directly construct symplectic forms on some 4-manifolds and to prove that log transforms of multiplicity 2 and 3 in certain cusp neighborhoods may be done in the symplectic category. We also develop techniques to study tight contact structures on lens spaces. We use these techniques to show that on any lens space there is a class $c in H^2(L(p,q))$ that is realized as the Euler class of a unique contact structure (if it is realized by one at all). For more results along these lines see my paper Tight contact structures on lens spaces. Also note there was an error in the proof of Lemma 5.9 in the dissertation (Lemma 3.6 in the paper). For a correction see the Erratum to tight contact structures on lens spaces.

One of the convexity arguments in chapter 3 is also incorrect. The result is still true and will be addressed in a subsequent paper. In is now known that all rational blowdowns may be performed symplectically. This is due to Margaret Symington, though the results in this thesis and the correction to chapter 3 mentioned above also give this complete result.

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