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September 2013 Minimality of symplectic fiber sums along spheres
Josef G. Dorfmeister
Asian J. Math. 17(3): 423-442 (September 2013).

Abstract

In this note we complete the discussion begun in A. I. Stipsicz, Indecomposability of certain Lefschetz fibrations, concerning the minimality of symplectic fiber sums. We find that for fiber sums along spheres the minimality of the sum is determined by the cases discussed in M. Usher, Minimality and symplectic sums, and one additional case: If $X{\#}_VY = Z {\#}V_{\mathbb{C}P^2}\mathbb{C}P^2$ with $V_{\mathbb{C}P^2}$ an embedded +4-sphere in class $[V_{\mathbb{C}P^2}] = 2[H] \in H_2(\mathbb{C}P_2, Z)$ and $Z$ has at least 2 disjoint exceptional spheres $E_i$ each meeting the submanifold $V_Z \subset Z$ positively and transversely in a single point, then the fiber sum is not minimal.

Citation

Download Citation

Josef G. Dorfmeister. "Minimality of symplectic fiber sums along spheres." Asian J. Math. 17 (3) 423 - 442, September 2013.

Information

Published: September 2013
First available in Project Euclid: 8 November 2013

zbMATH: 1284.53078
MathSciNet: MR3119794

Subjects:
Primary: 53D35, 53D45, 57R17

Rights: Copyright © 2013 International Press of Boston

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Vol.17 • No. 3 • September 2013
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