Demonstrates the construction of multiple symplectic tori in elliptic surfaces, indicating diverse geometrical structures.
We construct an infinite family of homotopic but pairwise smoothly non-isotopic symplectic tori in the rational elliptic surface E(1)=P²#9P̄². Furthermore, we show that any two of these tori are smoothly equivalent, i.e., there exists an orientation-preserving self-diffeomorphism of $E(1)$ that carries one torus to the other. Our construction can be generalized for many other symplectic $4$-manifolds, for example, the logarithmic transforms E(n)ₘ for integers $n,m>1$.
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B Park (2026) studied this question.
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