arXiv subjects

Han Lou

Publications and source records attributed to Han Lou.

4 recordsLinked to original sources

arXiv2026

Explicit Hamiltonian Classification in the $F_4(0)$ Toric Degeneration of $CP^2$

We give an explicit coordinate description of the Hamiltonian isotopy classes of the regular Lagrangian torus fibers of the smoothing $\widehat{F}_4(0)$ of the $F_4(0)$ toric degeneration, expressed in the explicit Oakley--Usher coordinates on $\CP^2(\sqrt2)$. For the wall fibers, they are not Hamiltonian isotopic to standard toric fibers, and no two distinct wall fibers are Hamiltonian isotopic. For the off-wall fibers, we find the standard toric fibers they are Hamiltonian isotopic to.

math.SG↗

arXiv2024

On Lagrangian Tori in $S^2\times S^2$

In [FOOO12], K. Fukaya, Y. Oh, H. Ohta, and K. Ono (FOOO) obtained the monotone symplectic manifold $S^2\times S^2$ by resolving the singularity of a toric degeneration of a Hirzebruch surface. They identified a continuum of toric fibers in the resolved toric degeneration that are not Hamiltonian isotopic to the toric fibers of the standard toric structure on $S^2\times S^2$. In this paper, we provide a comprehensive classification: for any toric fiber in FOOO's construction of $S^2\times S^2$, we determine whether it is Hamiltonian isotopic to a toric fiber of the standard toric structure of $S^2\times S^2$.

math.SG↗

arXiv2023

On the Hofer-Zehnder conjecture for semipositive symplectic manifolds

We show that, on a closed semipositive symplectic manifold with semisimple quantum homology, any Hamiltonian diffeomorphism possessing more contractible fixed points, counted homologically, than the total Betti number of the manifold, must have infinitely many periodic points. This generalizes to the semipositive setting the beautiful result of Shelukhin on the Hofer-Zehnder conjecture.

math.SG↗

arXiv2018

$\partial$-reducible handle additions

Let $M$ be a simple 3-manifold, and $F$ be a component of $\partial M$ of genus at least 2. Let $\alpha$ and $\beta$ be separating slopes on $F$. Let $M(\alpha)$ (resp. $M(\beta)$) be the manifold obtained by adding a 2-handle along $\alpha$ (resp. $\beta$). If $M(\alpha)$ and $M(\beta)$ are $\partial$-reducible, then the minimal geometric intersection number of $\alpha$ and $\beta$ is at most 8.

math.GT↗