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arxiv: math/0307029 · v1 · submitted 2003-07-02 · 🧮 math.GT · math.SG

Homologous Non-isotopic Symplectic Tori in Homotopy Rational Elliptic Surfaces

classification 🧮 math.GT math.SG
keywords symplectichomologousknottorielliptichomotopynon-isotopicrational
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Let E(1)_K denote the closed 4-manifold that is homotopy equivalent (hence homeomorphic) to the rational elliptic surface E(1) and is obtained by performing Fintushel-Stern knot surgery on E(1) using a knot K in S^3. We construct an infinite family of homologous non-isotopic symplectic tori representing a primitive homology class in E(1)_K when K is any nontrivial fibred knot in S^3. We also show how these tori can be non-isotopically embedded as homologous symplectic submanifolds in other symplectic 4-manifolds.

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