Homologous non-isotopic symplectic tori in a K3-surface

Mathematics – Geometric Topology

Scientific paper

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15 pages, 9 figures; v2: extended the main theorem, gave a second construction of symplectic tori, added a figure, added/updat

Scientific paper

10.1142/S021919970500174X

For each member of an infinite family of homology classes in the K3-surface E(2), we construct infinitely many non-isotopic symplectic tori representing this homology class. This family has an infinite subset of primitive classes. We also explain how these tori can be non-isotopically embedded as homologous symplectic submanifolds in many other symplectic 4-manifolds including the elliptic surfaces E(n) for n>2.

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