Geometric and Algebraic TopologyGeometry and complex manifoldsAlgebraic and Geometric Analysis
B. Park
2026.1.1Journal of Symplectic Geometry
Abstract
We construct an infinite family of homotopic but pairwise smoothly non-isotopic symplectic tori in the rational elliptic surface $E(1)=\mathbb{P}^2\#9\overline{\mathbb{P}}{}^2$. 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 $n,m>1$.
Citation format
PARK, B. Non-isotopic symplectic tori in elliptic surfaces. Journal of Symplectic Geometry, 2026, 23(6): 1377–1390.