Symplectic tori in rational elliptic surfaces

Details Symplectic tori in rational elliptic surfaces Symplectic tori in rational elliptic surfaces

2003-08-28

arxiv.org/abs/math/0308276v1

Math. Ann. 334 (2006), 679-691

Mathematics

Geometric Topology

8 pages, 3 figures

Scientific paper

10.1007/s00208-005-0724-5

Let E(1)_p denote the rational elliptic surface with a single multiple fiber f_p of multiplicity p. We construct an infinite family of homologous non-isotopic symplectic tori representing the primitive class [f_p] in E(1)_p when p>1. As a consequence, we get infinitely many non-isotopic symplectic tori in the fiber class of the rational elliptic surface E(1) (complex projective plane blown-up at nine branch points of a generic pencil of cubic curves). We also show how these tori can be non-isotopically and symplectically embedded in many other symplectic 4-manifolds.

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