English

Symplectic tori in rational elliptic surfaces

Geometric Topology 2007-05-23 v1 Symplectic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.math/0308276,
  title  = {Symplectic tori in rational elliptic surfaces},
  author = {Tolga Etgü and B. Doug Park},
  journal= {arXiv preprint arXiv:math/0308276},
  year   = {2007}
}

Comments

8 pages, 3 figures

R2 v1 2026-07-22T16:57:13.558Z