Asian Journal of Mathematics

Volume 17 (2013)

Number 3

Minimality of symplectic fiber sums along spheres

Pages: 423 – 442

DOI: http://dx.doi.org/10.4310/AJM.2013.v17.n3.a2

Author

Josef G. Dorfmeister (Department of Mathematics, North Dakota State University, Fargo N.D., U.S.A.)

Abstract

In this note we complete the discussion begun in [24] 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 [27] 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.

Keywords

symplectic manifolds, symplectic fiber sum, minimality

2010 Mathematics Subject Classification

53D35, 53D45, 57R17

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